My research is in Algebraic Geometry, with a focus on moduli theory. I primarily use techniques involving algebraic stacks. Much of my work lies in Enumerative Geometry, Intersection Theory, and the computation of invariants of algebraic stacks. More recently, I have also been exploring questions related to the fundamental group of schemes and stacks.
Below is a list of my publications and preprints.
1. The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves, 2025, published in Manuscripta Mathematica (Journal version).
Abstract: We study the integral Chow ring of the stack of n-pointed smooth hyperelliptic curves of genus g. We compute it for n=1,2 completely, while for 3<=n<=2g+2 we compute it up to the additive order of a signle class in degree 2. We obtain partial results also for n=2g+3. In particular, taking g=2, our results hold for the Chow ring of M_{2,n} for 1<=n<=7.
2. The Integral Chow Ring of the Stack of Hyperelliptic Prym Pairs I, with Alessio Cela, 2025, accepted in Mathematische Zeitschrift.
Abstract: This paper is the first in a series dedicated to computing the integral Chow rings of the moduli stacks of Prym pairs. In this work, we compute the Chow ring for Prym pairs arising from a single pair of Weierstrass points and from at most (g-1)/2 pairs when the genus g of the curve is odd.
Abstract: This paper is the third and final part of a series devoted to the description of the integral Chow rings of the moduli stacks of hyperelliptic Prym pairs. For a fixed genus $g$, there are two natural stacks, $\RH_g$ and $\wRH_g$, parametrizing hyperelliptic Prym pairs, with the former being the $\mu_2$-rigidification of the latter. Both decompose as the disjoint union of $\lfloor (g+1)/2 \rfloor$ components, denoted $\mathcal{RH}_g^n$ and $\wRH_g^n$ for $n = 1, \ldots, \lfloor (g+1)/2 \rfloor$. In this paper we present quotient stack descriptions of the components $\mathcal{RH}_g^n$ for even $g$ and compute their integral Chow rings, thereby completing the computation for all irreducible components of $\RH_g$. In addition, we give quotient stack presentations for all irreducible components of $\widetilde{\mathcal{RH}}_g$ and determine when the rigidification map $\widetilde{\mathcal{RH}}_g^n \to \RH_g^n$ is a root gerbe. We then use this to compute the Chow rings of $\wRH_g^n$ for all $g$ and $n$, with the sole exception of the case where $g$ is odd and $n=(g+1)/2$.
Finally, in the appendix, we discuss $G$-gerbes induced by an homomorphism of abelian groups $H \to G$ and an $H$-gerbe.
Abstract: This paper is the second in a series devoted to describing the integral Chow ring of the moduli stacks RH_g of hyperelliptic Prym pairs. For fixed genus g, the stack RH_g is the disjoint union of $\lfloor (g+1)/2 \rfloor$ components RH_g^n for $n = 1,...,\lfloor (g+1)/2 \rfloor$. In this paper, we compute the integral Chow rings of the components RH_g^{(g+1)/2} for odd g. Along the way, we also determine the integral Chow ring of the moduli stack of unordered pairs of two divisors on the projective line of the same even degree.
Abstract: We investigate monodromy groups arising in enumerative geometry, with a particular focus on how these groups are influenced by prescribed symmetries. To study these phenomena effectively, we work in the framework of moduli stacks rather than moduli spaces. This perspective proves broadly useful for understanding and constructing monodromy. We illustrate these ideas through several examples, with special attention to the 27 lines on a cubic surface, assuming the surface admits a given symmetry group.
Abstract: We study the stack H_{r,g,n} of n-pointed smooth cyclic covers of degree r between smooth curves of genus g and the projective line. We give two presentations of an open substack of H_{r,g,n} as a quotient stack, and we study its complement. Using this, we compute the integral Picard group of H_{r,g,n}. Moreover, we obtain a very explicit description of the generators of the Picard group, which have evident geometric meaning. As a corollary of the computation, we get the integral Picard group of the stack H_{g,n} of n-pointed hyperelliptic curves of genus g. Finally, taking g=2 and recalling that H_{2,n}=M_{2,n}, we obtain Pic(M_{2,n}).