papers and preprints

Published papers

1.  The Hodge structure of the intersection of three quadrics in an odd-dimensional projective space, Math. Ann. 273 (1986), no. 2, 277–285  

2.  On the Picard group of the moduli space for K-3 surfaces, Duke Math. J. 53 (1986), no. 1, 117–124.

3. On the Kodaira dimension of moduli spaces of abelian surfaces, Compositio Math. 72 (1989), no. 2, 121–163.

4.  Algebro-geometric analogues of Donaldson’s polynomials, Invent. Math. 107 (1992), no. 2, 351–395

5.  Donaldson’s polynomials for K3 surfaces, J. Differential Geom. 35 (1992), no. 2, 415–427.

6.  The irreducible components of moduli spaces of vector bundles on surfaces, Invent. Math. 112 (1993), no. 3, 585–613. 

7. Differential topology of complex surfaces - Elliptic surfaces with pg = 1: smooth classification, LNM 1545. Springer-Verlag, 1993

8. Relations among Donaldson polynomials of certain algebraic surfaces. I, Forum Math. 8 (1996), no. 1, 1–61.  

9.  Relations among Donaldson polynomials of certain algebraic surfaces. II, Forum Math. 8 (1996), no. 2, 135–193. 

10.  Moduli of vector bundles on projective surfaces: some basic results, Invent. Math. 123 (1996), no. 1, 141–207. 

11. The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebraic Geom. 6 (1997), no. 4, 599–644.  

12.  Moduli of vector-bundles on surfaces, Algebraic geometry—Santa Cruz 1995, 101–126, Proc. Sympos. Pure Math., 62,  AMS, 1997  

13.  Desingularized moduli spaces of sheaves on a K3, J. Reine Angew. Math. 512 (1999), 49–117. 

14.  A new six-dimensional irreducible symplectic variety, J. Algebraic Geom. 12 (2003), no. 3, 435–505. 

15. Hyperkähler manifolds and algebraic geometry, European Congress of Mathematics, 365–380, Eur. Math. Soc., Zurich, 2005.

16. Involutions and linear systems on holomorphic symplectic manifolds, Geom. Funct. Anal. 15 (2005), no. 6, 1223–1274.   

17. Irreducible symplectic 4-folds and Eisenbud-Popescu-Walter sextics, Duke Math. J. 134 (2006), no. 1, 99–137.

18. Irreducible symplectic 4-folds numerically equivalent to (K3)[2], Commun. Contemp. Math. 10 (2008), no. 4, 553–608.  

19. Dual double EPW-sextics and their periods, Pure Appl. Math. Q. 4 (2008), no. 2, 427–468.

20. EPW-sextics: taxonomy, Manuscripta Math. 138 (2012), no. 1, 221–272.

21. Higher-dimensional analogues of K3 surfaces, Current developments in algebraic geometry, MSRI Publ., 59, C.U.P. (2012), 257–293.  

22. Double covers of EPW-sextics, Michigan Math. J. 62 (2013), 143–184. 

23. Moduli of sheaves and the Chow group of K3 surfaces, J. Math. Pures Appl. 100 (2013), 701–718.

24. Pairwise incident planes and Hyperkähler four-folds, “A celebration of Algebraic Geometry” Clay Mathematics Proceedings 18 (2013), 553–566.

25. Computations with modified diagonals, Rendiconti Lincei Matematica e Applicazioni 25 (2014), 249–274.

26. Periods of double EPW-sextics,  Math. Z. 280 (2015),  485--524.

27. Moduli of double EPW-sextics,  Mem. Amer. Math. Soc. 240 (2016), no. 1136. 

28. Decomposable cycles and Noether-Lefschetz loci,  Doc. Math. 21 (2016), 661--687.

29. with R. Laza GIT versus Baily-Borel compactification for quartic K3 surfaces, Geometry of Moduli, Abel Symposia 14 (2018), 217--283. 

30. with R. Laza Birational geometry of the moduli space of quartic K3 surfaces, Compositio Mathematica 155 (2019), 1655--1710.

31. with O. Debarre, F. Han, C. Voisin Hilbert squares of K3 surfaces and Debarre--Voisin varieties, Journal de l'École polytechnique -  Mathématiques 7 (2020), 653--710.

32. with O. Debarre, F. Han, C. Voisin Hilbert squares of K3 surfaces and Debarre--Voisin varieties, Journal de l'École polytechnique -  Mathématiques 7 (2020), 653--710.

33. with R. Laza GIT versus Baily-Borel compactification for K3's which are double covers of P^1xP^1,  Adv. Math. 383 (2021), Paper No. 107680, 63 pp.

34. Compact tori associated to hyperkähler manifolds of Kummer type, 

 Int. Math. Res. Not. 2021, no. 16, 12356--12419.

35. Moduli of sheaves on K3's and higher dimensional HK varieties, Surveys in Differential Geometry XXIV (2021), 403--440.

36. Modular sheaves on hyperkähler varieties, Algebraic Geometry 9 (2022) 1--38.

37. with L. Flapan, E. Macrì, G. Saccà The geometry of antisymplectic involutions, I, Math. Z. 300 (2022), pp.~3457--3495. 

38. Rigid stable rank 4 vector bundles on HK fourfolds of Kummer type,  

Épijournal Géom. Algébrique [2023–2025], Special volume in honour of Claire Voisin, Art. 19, 51 pp.

39. Rigid stable vector bundles on hyperkähler varieties of type K3^[n], J. Inst. Math. Jussieu 23 (2024), no. 5, 2051--2080.

40. Theta groups and projective models of hyperkähler varieties, Perspectives on four decades of algebraic geometry. Vol. 2. In memory of Alberto Collino, 249--280. Progr. Math., 352 Birkhäuser/Springer (2025).

Preprints

with L. Flapan, E. Macrì, G. Saccà The geometry of antisymplectic involutions, II, arXiv:2309.02238 [math.AG].

Modular sheaves with many moduli, arXiv:2407.18101 [math.AG], to appear on Geometry and Topology.