Research
My research program investigates the geometry of moduli spaces of sheaves on projective varieties, with an emphasis on their global structure, including the description of irreducible components, their geometry, and decomposition phenomena.
A central part of my work consists of constructing and identifying new irreducible components of moduli spaces, as well as understanding their geometric properties and associated invariants, exploring interactions with Lefschetz-type properties and related algebraic structures.
More recently, I have been extending this line of research to the setting of algebraic supergeometry, studying vector bundles and moduli spaces on supervarieties, with the aim of establishing geometric foundations and new structural correspondences in this context, including connections with motivations from theoretical physics. On the algebraic side, embedding theorems for algebras with trace and supertrace, generalizing Cayley-Hamilton algebras, provide a bridge between this algebraic theory and supergeometry.
Publications
Preprints
- 2026
The moduli space of torsion-free sheaves with quasi-maximal third Chern class
with Marcos Jardim and Leonardo Oliveira. arXiv:2609.32668
- 2026
On supertrace embeddings: radical theory, Gelfand-Kirillov dimension, and Morita equivalence
with Claudemir Fidelis and L. Centrone.
Accepted
- 2026
Embedding theorems as a bridge between supertraces and supergeometry
with Claudemir Fidelis and L. Centrone. Advances in Theoretical and Mathematical Physics, to appear. arXiv:2506.20395
Published
- 2026
On higher Jacobians, Laplace equations, and Lefschetz properties
with Aline V. Andrade and Rodrigo Gondim. Bulletin of the London Mathematical Society 58(1). arXiv:2311.02178
- 2025
Splitting of supervector bundles on projective superspaces
with Ugo Bruzzo. Annali di Matematica Pura ed Applicata 204(6), 2543-2554. doi:10.1007/s10231-025-01581-0 arXiv:2501.10765
- 2024
A generalization of Cayley-Hamilton algebras and an introduction to their geometries
with Claudemir Fidelis and José Lucas Galdino. Israel Journal of Mathematics 262(1), 359-397. doi:10.1007/s11856-024-2614-0
- 2022
Irreducible components of the moduli space of rank 2 sheaves of odd determinant on projective space
with Marcos Jardim and Alexander S. Tikhomirov. Advances in Mathematics 402, 108363. doi:10.1016/j.aim.2022.108363 arXiv:1903.00292
- 2021
New moduli components of rank 2 bundles on projective space
with Marcos Jardim, Alexander S. Tikhomirov and Sergey A. Tikhomirov. Sbornik: Mathematics 212(11), 1503-1552. doi:10.1070/sm9490 arXiv:1702.06520
- 2020
The spectrum of torsion free sheaves on P3 and applications
Matemática Contemporânea 47, 1-20. doi:10.21711/231766362020/rmc471 arXiv:1903.04343
- 2019
Gaps in the number of generators of monomial Togliatti systems
with Aline V. Andrade and Rosa M. Miró-Roig. Journal of Pure and Applied Algebra 223(4), 1817-1831. doi:10.1016/j.jpaa.2018.07.009
- 2018
Lefschetz property and powers of linear forms in K[x,y,z]
with Aline V. Andrade. Forum Mathematicum 30(4), 857-865. doi:10.1515/forum-2017-0059 arXiv:1703.07598
Doctoral thesis
The Geometry of the Moduli Space of Torsion Free Sheaves on Projective Spaces. PhD thesis, Universidade Estadual de Campinas (UNICAMP), 2019. Advisor: Marcos Jardim. Sandwich period at Universitat de Barcelona with Rosa Maria Miró-Roig.