Research

My research focuses on moduli spaces and their invariants, like integral Picard groups, integral Chow(-Witt) rings, Brauer groups as well as more arithmetically-oriented cohomological invariants (a.k.a. unramified cohomology); most of my work so far consisted in explicitly compute (some of) these invariants for moduli of hyperelliptic curves, moduli of smooth/stable curves of low genus, quasi-polarized K3 surfaces and elliptic surfaces

The kind of techniques that I use range from the more abstract stack-theoretical methods to the more down-to-earth equivariant intersection theory. In my darkest times, I also use Mathematica for doing explicit computations involving localization formulas.

Research interests

  • Moduli spaces/stacks of curves, quasi-polarized K3 surfaces, Weierstrass fibrations.
  • Picard groups and integral Chow rings.
  • Equivariant intersection theory.
  • Cohomological invariants (a.k.a. unramified cohomology) of moduli stacks.
  • Brauer groups.
  • Chow-Witt groups.

Publications and preprints

  1. Cohomological invariants and Brauer groups of algebraic stacks in positive characteristic, joint with Roberto Pirisi, preprint (2022).
  2. The integral Chow rings of moduli of Weierstrass fibrations, joint with Samir Canning and Giovanni Inchiostro, preprint (2022).
  3. Intersection theory on moduli of smooth complete intersections, preprint (2022).
  4. Stable cuspidal curves and the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$, joint with Michele Pernice and Angelo Vistoli, preprint (2021).
  5. Equivariant Chow-Witt groups and moduli stacks of elliptic curves, joint with Lorenzo Mantovani, preprint (2021).
  6. Polarized twisted conics and moduli of stable curves of genus two, joint with Angelo Vistoli, preprint (2021)
  7. Cohomological invariants of root stacks and admissible double coverings, joint with Roberto Pirisi, Canadian Journal of Mathematics, https://doi.org/10.4153/S0008414X21000602 (2021).
  8. 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, https://doi.org/10.1090/tran/8354 (2020).
  9. Brauer groups of moduli of hyperelliptic curves via cohomological invariants, joint with Roberto Pirisi, Forum of Mathematics, Sigma, https://doi.org/10.1017/fms.2021.55 (2021).
  10. A complete description of cohomological invariants of even genus hyperelliptic curves, joint with Roberto Pirisi, Documenta Mathematica, https://doi.org/10.25537/dm.2021v26.199-230 (2021).
  11. Integral Picard group of quasi-polarized K3 surfaces of low degree, preprint (2019).
  12. Picard group of moduli of curves of low genus in positive characteristic, Manuscripta Mathematica, https://doi.org/10.1007/s00229-020-01212-3 (2020).
  13. Cohomological invariants of the stack of hyperelliptic curves of odd genus, Transformation Groups, https://doi.org/10.1007/s00031-020-09598-w (2020).
  14. The Chow ring of the stack of hyperelliptic curves of odd genus, Int. Math. Res. Not., https://doi.org/10.1093/imrn/rnz101 (2019).
  15. 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).