Submitted papers*

•  M. Corrêa, János Kollár, Homology fiber bundles of varieties, that are not topological fiber bundles,(arXiv) . 2026.

• M. Corrêa, S. Noja, Shifted Poisson unfoldings and quantum anomalies, (arXiv) 2026

• M. Corrêa, S. Noja, Compactified supermoduli space is almost never projected. (arXiv) .2026.

• M. Corrêa, S. Noja, Formal moduli and the splitting theory of supermanifolds, 2026. (arXiv).

• P. Barbassa, G. Barbosa, M. Corrêa. Stacky geometry and logarithmic topology of transversely affine foliations. (arXiv) 2026.

• A. Cavalcante, M. Corrêa, F. Lourenço, Elaheh Shahsavaripour,  Excess logarithmic residues for foliations by curves and applications. (arXiv). 2026.

• M. Corrêa, S. Noja, A categorical and algebro-geonetric theory of localization, 2026. (arXiv).

• M. Corrêa, Elaheh Shahsavaripour, Log Bott localization with non-isolated lci zero varieties, 2026. (arXiv).

• M. Corrêa,   Tangential arcs and discrepancies of rank-one foliations, (arXiv)* . 2026.  (initiated in 2020)

• M. Corrêa,   Foliated and Mather-Jacobian discrepancies via tangential arcs, (arXiv)* . 2026.  (initiated in 2020)

• M. Corrêa, Transversal unfoldings of derived Foliations, (arXiv)*. 2026.  (initiated in 2022)

• M. Corrêa, P. Perrella, S. Velazquez , The logarithmic leaf complex and foliated d-semistability. (arXiv)*.2026. 

• M. Corrêa ; A. Massarenti, Log-Conformal Projective Manifolds, 2026. (arXiv)*  (initiated in 2019)

• A. Altavilla, M. Corrêa,  Geometry of the Donaldson-Friedman pushout: Twistor degenerations and instanton charge, 2026. (arXiv)*.  (initiated in 2021)

• M. Corrêa, A Cech-Stokes Pushout Groupoid: log/Kummer Betti presenter for Stokes torsors. 2026.(arXiv)*.  (initiated in 2018)

• M. Corrêa,  M. Rodríguez. A Poisson-Poincaré-Dulac for  Poisson Connections, 2026. (arXiv)*.  (initiated in 2019)

• M. Corrêa, G. Nonato, A. Russi, A lower bound for the Milnor number of vector fields, 2026. (arXiv)*. (initiated in 2020)

* Disclaimer and acknowledgements. I moved to Italy in 2021, and due to the overwhelming bureaucracy and the necessary period of adaptation, some of my projects were put on hold. Only now, in 2026, has it become possible to resume and complete them. I am deeply grateful to my collaborators for their patience, understanding, and support throughout this period.

• O. Calvo-Andrade, M. Corrêa, M. Jardim, J. Seade, On the connectedness of the singular set of holomorphic foliations, 2025 (arXiv).

• M. Corrêa, T. Suwa. On functoriality of Baum-Bott residues, 2025. (arXiv)

• M. Corrêa, F. Lourenço, D. Machado. Log Baum-Bott Residues for foliations by curves, 2024. (arXiv)*. (initiated in 2018)

• M. Corrêa, G. Nonato, A higher-dimensional Van den Essen type formula for projective foliations and applications, 2024. (arXiv)*.   (initiated in 2022)

• L. Centrone, M. Corrêa,  Moduli, Deformations and Algebraic K-Theory of Graded PI-Algebras, 2024 (arXiv)* (initiated in 2021)

• M. Corrêa, A. Muniz, Holomorphic foliations of degree two and arbitrary dimension, 2023.  (arXiv)*. (initiated in 2021)

Publications:

1.  M. Corrêa; J. Seade, Indices and Residues: From Poincaré–Hopf to Baum–Bott, and Marco Brunella. In: Handbook of Geometry and Topology of Singularities VIII, Springer, 2025, pp. 441–489. (arXiv) 

Editors: José Luis Cisneros-Molina, Lê Dũng Tráng, José Seade

2. M. Corrêa, I. Vainsencher, Enumerative geometry of Legendrian foliations: a Tale of Contact.  Perspectives on four decades: Algebraic Geometry 1980-2020. In memory of Alberto Collino; Progress in Mathematics . Volume 351 , 2025.  (arXiv). (Original Paper).

Editors: Alberto Albano, Paolo Aluffi, Michele Bolognesi, Cinzia Casagrande, Elisabetta Colombo, Alberto Conte, Antonella Grassi, Claudio Pedrini, Gian Pietro Pirola, Alessandro Verra.

3. M. Corrêa, O. Calvo-Andrade, J. Fonseca-Quispe.  Dimension two holomorphic distributions on four-dimensional projective space.  (arXiv). 

Bulletin des Sciences Mathématiques. 2024.

4. M. Corrêa, D. Machado. Global residue formula for logarithmic indices of foliations, 2024. 

Communications in Analysis and Geometry (arXiv). 

5. M. Corrêa; M. Jardim, S. Marchesi, Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space. (arXiv).

 Revista Matemática Iberoamericana. 2023.

6. M. Corrêa,  A. Molinuevo, F. Quallbrunn, Families and unfoldings of singular holomorphic Lie Algebroids. 2023. 

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze .

7. M. Corrêa ; M. Jardim,  A. Muniz, Moduli of Distributions via Singular Schemes . 2022. 

Mathematische Zeitschrift.

8. M. Corrêa, Antonio M. Ferreira, Misha Verbitsky, Classification of holomorphic Pfaff systems on Hopf  manifolds. 

 European Journal of Mathematics.  2021.

9. M. Corrêa,  Antonio M. Ferreira,  F. Lourenço,  D. Machado , On Gauss-Bonnet and Poincaré-Hopf type  theorems for  complex  ∂-manifolds. 

 Moscow Mathematical Journal. 2021.

10. M. Corrêa , M. Soares, A. Fernandez-Perez, Brunella-Khanedani-Suwa variational residues  for invariants currents. 

 Journal of Singularities,  2021. 

11. M. Corrêa, O. Calvo-Andrade,  M. Jardim,  Codimension one distributions and stable rank 2 reflexive sheaves on threefolds. 

Annals of the Brazilian Academy of Sciences.  2021.

12. M. Corrêa ,  V.  Soares dos Reis,  A  singular Darboux  type theorem and  non-integrable  projective distributions of degree one. 

 B. de la Sociedad Matemática Mexicana.  2021.

13. M. Corrêa, Rational Morita equivalence for holomorphic Poisson modules,

  Advances in Mathematics. Volume 372, 7,  2020. 

14. M. Corrêa ; O. Calvo-Andrade, M. Jardim, Codimension one holomorphic distributions on projective three-spaces.  

 International Mathematics Research Notices.  Vol.  2020, 23, pg.  9011–9074. 2020.

15. M. Corrêa ; D. Machado, GSV-index for holomorphic Pfaff systems.  

Documenta Mathematica. 25, 1011-1027 , 2020.

16. A. Cavalcante, M. Corrêa, S. Marchesi, On holomorphic distributions on Fano threefolds,

Journal of Pure and Applied Algebra. vol. 224,   6,    2020. 

17. M. Corrêa  ; T. Suwa.  Localization of Bott-Chern classes and Hermitian residues.   

Journal of the London Mathematical Society.  vol. 101, 1, 349-372, 2020. 

18. M. Corrêa ; D. Machado, Residue formulas for logarithmic foliations and applications.

Transactions of the American Mathematical Society. vol.  371, 6403-6420,  2019.  

19.  M. Corrêa ;   F. Lourenço, Determination of Baum-Bott residues for  higher dimensional  foliations.  

Asian Journal of Mathematics. 2019.

20.  M. Corrêa ; A. Muniz, Polynomial bounds for automorphism groups of foliations. 

Revista Matemática Iberoamericana. 2019.

21. M. Corrêa ; C. Araujo, A. Massarenti, Codimension one Fano distributions on  Fano manifolds. 

Communications in Contemporary Mathematics, 2018.

22.  M. Corrêa ; L. Câmara,   Residues for maps generically  transversal to foliations.  

Proceedings of the American Mathematical Society.  146,  pg 5225-5234,   2018.

23.  M. Corrêa ; J-P. Brasselet; F. Lourenço, Residues for  flags of holomorphic foliations.  

Advances in Mathematics, vol. 320, n.7, 1158-1184,  2017. 

24. M. Corrêa  ; A. Fernandez-Perez; O. Calvo-Andrade, Higher codimensional holomorphic foliations with a Kupka set.  

International Journal of Mathematics, vol. 28, n.3,  2017.

25.  M. Corrêa  ; A. Fernandez-Perez; Absolutely k-convex domains and holomorphic foliations on homogeneous manifolds.

 Journal of the Mathematical Society of Japan. vol. 69, n.3,  1235-1246, 2017.

26.  M. Corrêa  ; A. M. Rodríguez ; F. Brochero Martinez;  Poincaré problem for weighted projective foliations. 

Bulletin Brazilian Mathematical Society , 48, (2), 219-235,  2017.

27.  M. Corrêa  ; A. M. Rodríguez;  M. G. Soares. A Bott type residues formula for  complex orbifolds.  

International Mathematics Reserch Notices, (10), 2889-2911, 2016. 

28. M. Corrêa  ; A. M. Ferreira; A. Fernandez-Perez, Classification of holomorphic distributions on Hopf manifolds. 

Mathematische Annalen. v. 365, (1) , 579-593, 2016.

29. M. Corrêa ; Rank two nilpotent co-Higgs sheaves on complex surfaces, 

Geometriae Dedicata,  183, (1), 25-31, 2016.

30.  M. Corrêa  ; A. M. Rodríguez; Residue formula for Morita-Futaki-Bott invariants on complex orbifolds - 

Comptes Rendus Mathematique.  (354), 1109-1113, 2016.

31.  M. Corrêa  ; L. G. Maza, Engel Theorem through singularities. 

Bulletin des Sciences Mathématiques,  140, (6),  675-686. 2016.

32.  M. Corrêa  ; A. Fernandez-Perez; O. Calvo-Andrade, On non-Kupka points of codimension one foliations on P3. 

Annals of the Brazilian Academy of Sciences. vol. 88, n.4, 2016. 

33. M. Corrêa Jr ; M. Jardim ; R. Vidal . On the Singular scheme of split foliations, 

Indiana University Mathematics Journal,  64 No. 5  1359–1381, 2015.

34.  M. Corrêa Jr ; L. G. Maza, M. G. Soares, Hypersurfaces Invariant by Pfaff Equations,

Communications in Contemporary Mathematics, 17, 1450051. 2015.

35.  M. Corrêa Jr ; G. N. Costa ;A.  Fernandez-Perez ; R. Vidal . Foliations by curves with curves as singularities, 

Annales de l'institut Fourier,  64 n.4 , pg. 1781-1805- 2014.

36. M. Corrêa Jr ; T. Fassarela,  On the order of the automorphism group of foliations,

Mathematische Nachrichten  , 287, No 16, 1795-1803, 2014.

37.  M. Corrêa Jr ; C. Araujo. On degeneracy scheme of maps of vector bundles and application to holomorphic foliations, 

Mathematische  Zeitschrift , v 276 , issue 1-2, pp. 505-515, 2013.

38.  M. Corrêa Jr ; M. G. Soares .Inequalities for characteristic numbers of flags of distributions and foliations, 

International Journal of Mathematics. v 24, 1350093, 2013. (Errata: a typo fixed)

39.  M. Corrêa Jr ; SOARES, M. G. . A note on Poincaré s problem for quasi-homogeneous foliations. 

Proceedings of the American Mathematical Society, v. 145, p. 1,  2012.

40.  M. Corrêa Jr ; M. Jardim . Bounds for sectional genera of varieties invariant under Pfaff fields.

Illinois Journal of Mathematics, vol. 56-2,  pg 343-352, 2012.

41. M. Corrêa Jr ; Maza, L.G. ; M. G. Soares . Algebraic integrability of polynomial differential r-forms. 

Journal of Pure and Applied Algebra, v. 215, p. 2290-2294, 2011.

42. M. Corrêa Jr . An improvement to Lagutinskii-Pereira integrability Theorem. 

Mathematical Research Letters, v. 18, p. 645-661, 2011.

43.  M.  Corrêa , M. G. Soares ; . A Poincaré type inequality for one-dimensional multiprojective foliations. 

Bulletin Brazilian Mathematical Society, v. 42, p. 485-503, 2011.

44. M. Corrêa Jr . Darboux Integrability For Polynomial Vector Fields Invariant Under Action of Finite Group. 

Qualitative Theory of Dynamical Systems, v. 11, p. 159-166, 2011.

45.  M. Corrêa Jr ; M. G. Soares . Counting hypersurfaces invariant by one-dimensional complex foliations. 

London Mathematical Society. Lecture Note Series, v. 308, p. 104-113, 2010.

46.  M. Corrêa Jr . Darboux-Jouanolou- Ghys integrability for one-dimensional foliations on toric varieties. 

Bulletin des Sciences Mathématiques , v. 134, p. 693-704, 2010.