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 for doing explicit computations involving localization formulas.

Research interests

  • Moduli of curves, quasi-polarized K3 surfaces, Weierstrass fibrations, stable maps.
  • Picard groups, integral Chow rings, equivariant intersection theory.
  • Cohomological invariants (a.k.a. unramified cohomology) and Brauer groups.
  • Quadratic intersection theory and Chow-Witt groups.
  • Logarithmic geometry, compactification of Prym varieties.

Preprints

  1. A criterion for smooth weighted blow-downs, joint with Veronica Arena, Giovanni Inchiostro, Siddharth Mathur, Stephen Obinna and Michele Pernice (2023).
  2. Effective morphisms and quotient stacks, joint with Giovanni Inchiostro (2023).
  3. Degenerations of twisted maps to algebraic stacks, joint with Giovanni Inchiostro (2022).
  4. Cohomological invariants and Brauer groups of algebraic stacks in positive characteristic, joint with Roberto Pirisi (2022).
  5. Polarized twisted conics and moduli of stable curves of genus two, joint with Angelo Vistoli (2021)
  6. Integral Picard group of some stacks of polarized K3 surfaces of low degree (2019).

Publications

  1. Integral Picard group of moduli of polarized K3 surfaces, joint with Roberto Fringuelli and Angelo Vistoli, to appear on Bulletin of the LMS (2023).
  2. The integral Chow rings of moduli of Weierstrass fibrations, joint with Samir Canning and Giovanni Inchiostro, to appear on Transactions of the AMS (2022).
  3. Stable cuspidal curves and the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$, joint with Michele Pernice and Angelo Vistoli, to appear on Geometry & Topology (2022).
  4. Intersection theory on moduli of smooth complete intersections, Mathematische Zeitschrift, journal version, (2022).
  5. Equivariant Chow-Witt groups and moduli stacks of elliptic curves, joint with Lorenzo Mantovani, Documenta Mathematica, journal version, (2021).
  6. Cohomological invariants of root stacks and admissible double coverings, joint with Roberto Pirisi, Canadian Journal of Mathematics, journal version, (2021).
  7. Brauer groups of moduli of hyperelliptic curves via cohomological invariants, joint with Roberto Pirisi, Forum of Mathematics, Sigma, journal version, (2021).
  8. A complete description of cohomological invariants of even genus hyperelliptic curves, joint with Roberto Pirisi, Documenta Mathematica, journal version, (2021).
  9. 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).
  10. Picard group of moduli of curves of low genus in positive characteristic, Manuscripta Mathematica, journal version, (2020).
  11. Cohomological invariants of the stack of hyperelliptic curves of odd genus, Transformation Groups, journal version, (2020).
  12. The Chow ring of the stack of hyperelliptic curves of odd genus, International Mathematics Research Notices, journal version, (2019).
  13. 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).