Publications

Research papers in mathematical journals, preprints, works in progress:

1. Marian Aprodu, Gavril Farkas, Claudiu Raicu, Alexander I. Suciu. Non-vanishing resonance and Hilbert series of Koszul modules. work in progress.

2. Marian Aprodu, Andrea Bruno, Edoardo Sernesi. The second syzygy schemes of curves of large degree. work in progress.

3. Marian Aprodu, Yoengrak Kim. Resonance, syzygies and rank-3 Ulrich bundles on the del Pezzo threefold V5. preprint arXiv:2404.12051. link

4. Marian Aprodu, Gavril Farkas, Claudiu Raicu, Alexander I. Suciu. Reduced resonance schemes and Chen ranks.  to appear in Journal für die reine und angewandte Mathematik, link

5. Marian Aprodu, Laura Filimon: Sections of K3 surfaces with Picard number two and Mercat’s conjecture. to appear in Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. link 

6. Marian Aprodu, Gavril Farkas, Claudiu Raicu, Alessio Sammartano, Alexander I. Suciu.  Higher resonance schemes and Koszul modules of simplicial complexes. Journal of Algebraic Combinatorics (2024) DOI:10.1007/s10801-024-01313-2.  link

7. Marian Aprodu, Gavril Farkas, Claudiu Raicu, Jerzy Weyman. Koszul modules with vanishing resonance in algebraic geometry. Selecta Mathematica, Volume 30, article number 24, (2024) DOI:10.1007/s00029-023-00912-4. link

8. Marian Aprodu, Gavril Farkas, Stefan Papadima, Claudiu Raicu, Jerzy Weyman. Topological invariants of groups and Koszul modules. Duke Mathematical Journal, 171 (10), (2022) 2013 - 2046, DOI:10.1215/00127094-2022-0010. link

9. Marian Aprodu, Indranil Biswas, Sorin Dumitrescu, Sebastian Heller. On the monodromy map for the logarithmic differential systems, Bulletin de la Société Mathématique de France 150 (3), (2022) 543-568, DOI:10.24033/bsmf.2854. link

10. Marian Aprodu, Yeongrak Kim. On the Borisov-Nuer conjecture and the image of the Enriques-to-K3 map. Mathematische Nachrichten, Volume 293, Issue 6 (2020) 1044-1052, DOI:10.1002/mana.201900226 link

11. Marian Aprodu, Gianfranco Casnati, Laura Costa, Rosa Maria Miro-Roig, Monserrat Teixidor i Bigas. Theta divisors and Ulrich bundles on geometrically ruled surfaces. Annali di Matematica Pura ed Applicata, Volume 199 (2020) 199–216, DOI:10.1007/s10231-019-00873-6  link

12. Marian Aprodu, Gavril Farkas, Stefan Papadima, Claudiu Raicu, Jerzy Weyman. Koszul modules and Green's conjecture. Inventiones Mathematicae, Volume 218, Issue 3 (2019) 657-720, DOI:10.1007/s00222-019-00894-1  link

13. Marian Aprodu, Sukmoon Huh, Francesco Malaspina, Joan Pons-Llopis. Ulrich bundles on smooth projective varieties of minimal degree. Proceedings of the American Mathematical Society, Volume 147, Number 12, (2019) 5117–5129, DOI:10.1090/proc/14640  link

14. Marian Aprodu, Andrea Bruno, Edoardo Sernesi. A characterization of bielliptic curves via syzygy schemes. Journal of Pure and Applied Algebra 223 (2019) 4690-4700, DOI:10.1016/j.jpaa.2019.02.011 link

15. Marian Aprodu, Laura Costa, Rosa Maria Miro-Roig. Rank two vector bundles on non-minimal ruled surfaces. Transactions of the American Mathematical Society, 370 (2018) 3913-3929, DOI:10.1090/tran/7062  link

16. Marian Aprodu, Laura Costa, Rosa Maria Miro-Roig. Ulrich bundles on ruled surfaces. Journal of Pure and Applied Algebra, 222:1 (2018) 131-138, DOI:10.1016/j.jpaa.2017.03.007 link

17. Marian Aprodu, Gavril Farkas, Angela Ortega. Minimal resolutions, Chow forms of K3 surfaces and Ulrich bundles. Journal für die reine und angewandte Mathematik, 730 (2017) 225-250, DOI:10.1515/crelle-2014-0124 link

18. Marian Aprodu, Edoardo Sernesi. Excess dimension for secant loci in symmetric products of curves. Collectanea Mathematica, 68:1 (2017) 1-7, DOI:10.1007/s13348-016-0166-2 link

19. Marian Aprodu, Luigi Lombardi. On the vanishing of Koszul cohomology of abelian varieties. Bulletin of the London Mathematical Society 48:2 (2016) 280-290, DOI:10.1112/blms/bdw004 link

20. Marian Aprodu, Marius Marchitan. Prioritary omalous bundles on Hirzebruch surfaces. Journal of Geometry and Physics 99 (2016) 1-9, DOI:10.1016/j.geomphys.2015.09.004 link

21. Marian Aprodu, Edoardo Sernesi. Secant spaces and syzygies of special line bundles on curves. Algebra & Number Theory 9:3 (2015) 585-600, DOI:10.2140/ant.2015.9.585 link

22. Monica Alice Aprodu, Marian Aprodu. Holomorphic vector bundles on Kaehler manifolds and totally geodesic foliations on Euclidean open domains. Differential Geometry and its Applications 39 (2015) 10-19, DOI:10.1016/j.difgeo.2015.01.002 link

23. Marian Aprodu, Matei Toma. Boundedness for some rationally connected threefolds in P6. Communications in Algebra, 42:9 (2014) 3876-3882, DOI:10.1080/00927872.2013.796963 link

24. Marian Aprodu, Ruxandra Moraru, Matei Toma. Two-dimensional moduli spaces of vector bundles over Kodaira surfaces. Advances in Mathematics 231 (2012) 1202-1215, DOI:10.1016/j.aim.2012.06.024 link

25. Marian Aprodu, Marius Marchitan. A note on vector bundles on Hirzebruch surfaces. Comptes Rendus Mathématique 349, no 11-12 (2011) 687-690, DOI:10.1016/j.crma.2011.04.013 link

26. Marian Aprodu, Gavril Farkas. Green's Conjecture for curves on arbitrary K3 surfaces. Compositio Mathematica 147 (2011) 839-851, DOI:10.1112/S0010437X10005099  link

27. Marian Aprodu, Daniel Naie. Enriques diagrams and log-canonical thresholds of curves on smooth surfaces. Geometriae Dedicata 146 (2010) 43-66, DOI:10.1007/s10711-009-9425-7 link

28. Marian Aprodu, Gianluca Pacienza. The Green Conjecture for Exceptional Curves on a K3 Surface. International Mathematics Research Notices (IMRN) (2008) nr. 14 Vol. 2008, article ID rnn043, 25 pages - Corrigendum and Addendum, International Mathematics Research Notices (2012) nr. 5, 1195-1197, DOI:10.1093/imrn/rnn043 link1 link2

29. Marian Aprodu, Stefan Kebekus, Thomas Peternell. Galois coverings and endomorphisms of projective varieties. Mathematische Zeitschrift 260 (2008) no.2, 431-449, DOI:10.1007/s00209-007-0282-5 link

30. Marian Aprodu, Jan Nagel. Non-vanishing for Koszul cohomology of curves. Commentarii Mathematici Helvetici 82 No. 3 (2007) 617-628, DOI:10.4171/CMH/104 link

31. Marian Aprodu. Remarks on syzygies of d-gonal curves. Mathematical Research Letters 12 No. 3 (2005) 387-400 DOI:10.4310/MRL.2005.v12.n3.a9 link

32. Marian Aprodu. Green-Lazarsfeld gonality conjecture for a generic curve of odd genus. International Mathematics Research Notices (IMRN) 63 (2004) 3409-3414, DOI:10.1155/S107379280414035X link

33. Marian Aprodu, Jan Nagel. A Lefschetz type result for Koszul cohomology. Manuscripta Mathematica 114 (2004) 423-430, DOI:10.1007/s00229-004-0467-8 link

34. Marian Aprodu, Matei Toma. Une note sur les fibrés holomorphes non-filtrables. Comptes Rendus Mathématique 336 No. 7 (2003) 581-584, DOI:10.1016/S1631-073X(03)00139-0 link

35. Marian Aprodu, Claire Voisin. Green-Lazarsfeld's conjecture for generic curves of large gonality. Comptes Rendus Mathématique 336 No. 4 (2003) 335-339, DOI:10.1016/S1631-073X(03)00062-1 link

36. Marian Aprodu. On the vanishing of higher syzygies of curves. II. Mathematische Zeitschrift 243 No. 4 (2003) 775-778, DOI:10.1007/s00209-002-0467-x link

37. Marian Aprodu, Vasile Brinzanescu. On the holomorphic rank-2 vector bundles with trivial discriminant over non-Kaehler elliptic bundles. Journal of Mathematics of Kyoto University (JKYAMZ) 42 No. 4 (2002) 617-623, DOI:10.1215/kjm/1250283829 link

38. Marian Aprodu, Vasile Brinzanescu, Matei Toma. Holomorphic vector bundles over primary Kodaira surfaces. Mathematische Zeitschrift 242 No. 1 (2002) 63-73, DOI:10.1007/s002090100307 link

39. Marian Aprodu. On the vanishing of higher syzygies of curves. Mathematische Zeitschrift 241 No. 1 (2002) 1-15, DOI:10.1007/s002090100 link

40. Monica Alice Aprodu, Marian Aprodu, Vasile Brinzanescu. A class of harmonic maps and minimal submanifolds. International Journal of Math. 11 No. 9 (2000) 1177-1191, DOI:10.1142/S0129167X0000057X link

41. Monica Alice Aprodu, Marian Aprodu. Implicitly defined harmonic PHH submersions. Manuscripta Mathematica 100 (1999) 103-121, DOI:10.1007/s002290050198 link

42. Marian Aprodu, Vasile Brinzanescu. Moduli spaces of vector bundles over ruled surfaces. Nagoya Mathematical Journal 154 (1999) 111-122, DOI:10.1017/S0027763000025332 link

43. Marian Aprodu. An Appell-Humbert theorem for hyperelliptic surfaces. Journal of Mathematics of Kyoto University (JKYAMZ) 38 No. 1 (1998) 101-121, DOI:10.1215/kjm/1250518162 link

44. Marian Aprodu, Vasile Brinzanescu. Existence of stable rank-2 vector bundles over ruled surfaces. Collection of papers in memory of Martin Jurchescu. Revue Roumaine de Mathématiques Pures et Appliquées 43 No. 1-2 (1998) 47-56.

45. Marian Aprodu, Vasile Brinzanescu. Stable rank-2 vector bundles over ruled surfaces. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 325 (1997) 295-300, DOI:10.1016/S0764-4442(97)83959-6 link

46. Marian Aprodu, Vasile Brinzanescu. Numerical invariants and stability of 2-vector bundles over ruled surfaces. Analele Științifice ale Universității Ovidius Constanța 5 No. 2 (1997) 9-16.

47. Marian Aprodu, Vasile Brinzanescu. Fibrés vectoriels de rang deux sur les surfaces réglées. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 323 (1996) 627-630.

Research and expository papers in conference proceedings and special volumes, book chapters:

48. Marian Aprodu, Victor Vuletescu. Indecomposable filtrable vector bundles on Oeljeklaus-Toma manifolds. Revue Roumaine de Mathématiques Pures et Appliquées, 65 No. 3 (2020) 227-234, Special volume dedicated to Professor Vasile Brînzănescu on his 75th birthday (Guest Editor: Liviu Ornea) link

49. Marian Aprodu, Yeongrak Kim. Ulrich line bundles on Enriques surfaces with a polarization of degree four. Annali del'Universita di Ferrara, 63:1 (2017) 9-23, Special volume dedicated to the memory of A. Lascu (Editor: Paltin Ionescu), DOI:10.1007/s11565-017-0269-z link

50. Marian Aprodu, Gavril Farkas, Angela Ortega. Restricted Lazarsfeld-Mukai bundles and canonical curves. Advanced Studies in Pure Mathematics (Math. Soc. Japan) 69 (2016) 303-322, Development of Moduli Theory, Special volume on the occasion of Mukai's 60th birthday (Editors: Osamu Fujino, Shigeyuki Kondô, Atsushi Moriwaki, Masa-Hiko Saito, Kōta Yoshioka), ISBN:978-4-86497-032-7. link

51. Marian Aprodu. Polynomial equations and vector bundles. On Form and Pattern, Ed. Acad. Române (2015) 77-82, Humboldt Symposium, Bucharest, May 29-31, 2014 (Editors: Cătălin Vasilescu, Maria-Luisa Flonta, Ioana Crăciun), ISBN: 978-973-27-2531-3 link

52. Marian Aprodu. Ulrich bundles on K3 surfaces. Oberwolfach Reports 11:3 (2014), Classical Algebraic Geometry (Editors: Olivier Debarre, David Eisenbud, Gavril Farkas, Ravi Vakil),  DOI: 10.4171/OWR/2014/31 link

53. Marian Aprodu. Lazarsfeld-Mukai bundles and applications. II. in: Bridging Algebra, Geometry, and Topology, Springer Proceedings in Mathematics & Statistics, Vol. 96 (2014) 11-20, Proceedings of the Conference "Experimental and Theoretical Methods in Algebra, Geometry and Topology", Eforie Nord, June 21-24, 2013 (Editors: Ibadula, Denis, Veys, Willem), DOI:10.1007/978-3-319-09186-0_2 link

54. Marian Aprodu. Lazarsfeld-Mukai bundles and applications. in: Peeva, Irena (ed.), Commutative algebra. New York, NY: Springer (2013) 1-23, Expository papers dedicated to David Eisenbud on the occasion of his 65th birthday (Editor: Irena Peeva), DOI:10.1007/978-1-4614-5292-8_1 link

55. Marian Aprodu, Gavril Farkas. Green's Conjecture for general covers. Contemporary Mathematics, AMS, Vol. 564 (2012) 211-226, Proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21–24, 2010, at the University of Georgia (Editors: Valery Alexeev, Angela Gibney, Elham Izadi, János Kollár, Eduard Looijenga ), DOI:10.1090/conm/564  link

56. Marian Aprodu, Vasile Brinzanescu, Marius Marchitan. Rank-two vector bundles on Hirzebruch surfaces. Central European Journal of Mathematics 10 No. 4 (2012) 1321-1330, Topical Issue: Instantons, coherent sheaves and their moduli spaces (Editors: Dimitri Markushevich, Alexander S. Tikhomirov, Misha Verbitsky), DOI:10.2478/s11533-012-0046-2 link

57. Marian Aprodu, Gavril Farkas. Koszul cohomology and applications to moduli. in: Grassmannians, vector bundles and moduli spaces, Clay Mathematics Proccedings, AMS, Vol. 14 (2011) 25-50, Clay Mathematics Institute Workshop Moduli Spaces of Vector Bundles, with a View Towards Coherent Sheaves October 6–11, 2006, Cambridge, Massachusetts (Editors: David A. Ellwood Emma Previato), ISBN: 978-0-8218-5205-7 link

58. Marian Aprodu, Vasile Brinzanescu. Beilinson type spectral sequences on scrolls. Moduli spaces and vector bundles. London Mathematical Society Lecture Note Series 359, Cambridge University Press (2009) 426-436, VBAC workshop in honor of Peter Newstead 65th anniversary, CIMAT Guanajuato, December 2006 (Editors: Leticia Brambila-Paz, Steven B. Bradlow, Oscar García-Prada, S. Ramanan), DOI:10.1017/CBO9781139107037.014 link

59. Marian Aprodu. Brill-Noether theory for curves on K3 surfaces. Contemporary geometry and topology and related topics, Cluj Univ. Press, Cluj-Napoca (2008) 1-12, Proceedings of the 8th International Workshop on Differential Geometry and its Applications, Cluj, August 19-25, 2007 (Editors: Dorin Andrica, Sergiu Moroianu), ISBN: 978-973-610-725-2 link

60. Marian Aprodu. Geometry of curves and Koszul cohomology. Modern trends in geometry and topology, Cluj Univ. Press, Cluj-Napoca (2006) 37-45,  Proceedings of the 7th International Workshop on Differential Geometry and its Applications, Deva, September 5-11, 2005 (Editors: Dorin Andrica, Paul Blaga, Sergiu Moroianu), ISBN: 973-610-429-X, 978-973-610-429-9 link

61. Marian Aprodu. On Green and Green-Lazarsfeld conjectures for generic d-gonal curves. Oberwolfach Reports No. 7 (2005) 427-430, Komplexe Algebraische Geometrie (Editors: Gang Tian, Fabrizio Catanese, Yujiro Kawamata, Eckart Viehweg), DOI: 10.4171/OWR/2005/07  link

Research monographs:

1. Marian Aprodu, Jan Nagel. Koszul Cohomology and Algebraic Geometry. University Lecture Series, vol. 52, 2010, AMS, 125 pp, ISBN-10: 0-8218-4964-6, ISBN-13: 978-0-8218-4964-4, DOI:10.1090/ulect/052 link

Textbooks:

1. Marian Aprodu. Noțiuni de Geometrie Algebrică. Ed. Fundației Univ. "Dunărea de Jos" Galați, 2008, ISBN: 978-973-627-425-1.

2. Marian Aprodu. Geometria Varietăților Torice. Ed. Acad. Române, 2008, ISBN: 978-973-27-1697-7.

Theses:

1. Marian Aprodu. Sur quelques problèmes de géométrie complexe (french). Habilitation thesis, Institut Fourier, Grenoble 2002. link file

2. Marian Aprodu. Fibrate vectoriale pe varietãţi complexe (romanian). PhD thesis, Institutul de Matematicã al Academiei Române, București 1996 (advisor Vasile Brinzanescu). file

Paper reviews on MathSciNet.