Research

My research focuses on moduli spaces and their geometry. This means that I am interested in constructing them, compactifying them and in computing some of their invariants (e.g. Chow groups, unramified cohomology, Brauer groups).

The kind of techniques that I use include stack-theoretical methods, logarithmic geometry, equivariant intersection theory and Galois cohomology. In my darkest times, I also use Mathematica or Sage for doing explicit computations (e.g. those that involve localization formulas).

Research interests

  • Moduli of curves, surfaces and stable maps.
  • Intersection theory.
  • Cohomological invariants (a.k.a. unramified cohomology) and Brauer groups.
  • Algebraic stacks and good moduli spaces.
  • Logarithmic geometry.

Preprints

  1. Cohomological invariants of $\mathscr{M}_{3,n}$ via level structures (2025)
  2. Integral Chow rings of modular compactifications of $\mathcal{M}_{1,n\leq 6}$, joint with Luca Battistella (2025).
  3. Stable maps to quotient stacks with a properly stable point, joint with Giovanni Inchiostro (2024).
  4. A criterion for smooth weighted blow-downs, joint with Veronica Arena, Giovanni Inchiostro, Siddharth Mathur, Stephen Obinna and Michele Pernice (2023).
  5. Degenerations of twisted maps to algebraic stacks, joint with Giovanni Inchiostro (2022).

Publications

Years in brackets below refer to when the first version was uploaded on arXiv.

  1. Wall-crossing integral Chow rings of $\overline{\mathcal{M}}_{1,n}$, joint with Luca Battistella, Forum of Mathematics, Sigma, journal version (2024).
  2. The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves, joint with Roberto Pirisi, Compositio Mathematica, journal version(2024).
  3. Effective morphisms and quotient stacks, joint with Giovanni Inchiostro, International Mathematics Research Notices, journal version (2023).
  4. Integral Picard group of moduli of polarized K3 surfaces, joint with Roberto Fringuelli and Angelo Vistoli, Bulletin of the LMS, journal version (2023).
  5. Cohomological invariants and Brauer groups of algebraic stacks in positive characteristic, joint with Roberto Pirisi, Algebraic Geometry, journal version (2022).
  6. The integral Chow rings of moduli of Weierstrass fibrations, joint with Samir Canning and Giovanni Inchiostro, Transactions of the AMS, journal version (2022).
  7. Intersection theory on moduli of smooth complete intersections, Mathematische Zeitschrift, journal version, (2022).
  8. Stable cuspidal curves and the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$, joint with Michele Pernice and Angelo Vistoli, Geometry & Topology, journal version (2021).
  9. Polarized twisted conics and moduli of stable curves of genus two, joint with Angelo Vistoli, to appear on Arkiv för Matematik (2021)
  10. Equivariant Chow-Witt groups and moduli stacks of elliptic curves, joint with Lorenzo Mantovani, Documenta Mathematica, journal version, (2021).
  11. Cohomological invariants of root stacks and admissible double coverings, joint with Roberto Pirisi, Canadian Journal of Mathematics, journal version, (2020).
  12. Brauer groups of moduli of hyperelliptic curves via cohomological invariants, joint with Roberto Pirisi, Forum of Mathematics, Sigma, journal version, (2021).
  13. Integral Chow ring of the stack of smooth non-hyperelliptic curves of genus three, joint with Damiano Fulghesu and Angelo Vistoli, Transactions of the AMS, journal version, (2020).
  14. A complete description of cohomological invariants of even genus hyperelliptic curves, joint with Roberto Pirisi, Documenta Mathematica, journal version, (2019).
  15. Integral Picard group of some stacks of polarized K3 surfaces of low degree, Journal of Pure and Applied Algebra, journal version (2019).
  16. Picard group of moduli of curves of low genus in positive characteristic, Manuscripta Mathematica, journal version, (2018).
  17. Cohomological invariants of the stack of hyperelliptic curves of odd genus, Transformation Groups, journal version, (2018).
  18. The Chow ring of the stack of hyperelliptic curves of odd genus, International Mathematics Research Notices, journal version, (2018).
  19. On quantum and relativistic mechanical analogues in mean field spin models, joint with Adriano Barra, Francesco Guerra and Antonio Moro, Proc. R. Soc. A 470: 20140589 (2014).