Related papers: Intersection theory on moduli of smooth complete i…

We construct an integral model of the perfectoid modular curve. Studying this object, we prove some vanishing results for the coherent cohomology at perfectoid level. We use a local duality theorem at finite level to compute duals for the…

We describe the Chow rings of moduli spaces of ordered configurations of points on the projective line for arbitrary (sufficiently generic) stabilities. As an application, we exhibit such a moduli space admitting two small…

For any smooth connected linear algebraic group G over an algebraically closed field k, we describe the Picard group of the universal moduli stack of principal G-bundles over pointed smooth k-projective curves.

The main objective of this paper is to give a summary of our recent work on recursion formulae for intersection numbers on moduli spaces of curves and their applications. We also present a conjectural relation between tautological rings and…

We develop a formula (Theorem 5.1) which allows to compute top Chern classes of vector bundles on the vanishing locus $V(s)$ of a section of this bundle. This formula particularly applies in the case when $V(s)$ is the union of locally…

We study the stack $\mathcal{H}_{r,g,n}$ 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 $\mathcal{H}_{r,g,n}$ as a quotient…

In this paper, we study the moduli space of quasi-polarized complex K3 surfaces of degree 6 and 8 via geometric invariant theory. The general members in such moduli spaces are complete intersections in projective spaces and we have natural…

We introduce the notion of a generalized intersection pairing for an Artin stack with a proper good moduli space and nonempty stable part. For the moduli stack of semistable bundles over a smooth projective curve, there are four known…

Let the bielliptic locus be the closure in the moduli space of stable curves of the locus of smooth curves that are double covers of genus 1 curves. In this paper we compute the class of the bielliptic locus in \bar{M}_3 in terms of a…

Let $\Gamma$ be a finite-index subgroup of the mapping class group of a closed genus $g$ surface that contains the Torelli group. For instance, $\Gamma$ can be the level $L$ subgroup or the spin mapping class group. We show that…

We determine the action of the product of symmetric groups on the cohomology of certain moduli of weighted pointed rational curves. The moduli spaces that we study are of stable rational curves with m+n marked points where the first m…

Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G/H defined by a generic collection of sections from G-invariant linear systems. Whenever nonempty, all such complete…

We construct the moduli stack of torsors over the formal punctured disk in characteristic p > 0 for a finite group isomorphic to the semidirect product of a p-group and a tame cyclic group. We prove that the stack is a limit of separated…

We study moduli spaces of a class of three dimensional N=4 gauge theories which are in one-to-one correspondence with a certain set of ordered pairs of integer partitions. It was found that these theories can be realised on brane intervals…

We study the moduli space F_{2d} of polarised K3 surfaces of degree 2d. We compute all relations between Noether-Lefschetz divisors on these moduli spaces for d up to around 50. This leads to a very concrete description of the rational…

For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in P^N is quasi-projective. ----- Pour certaines valeurs des degres des equations, on…

By associating to a curve C of genus g=2k and a pencil of degree d=k+1 the so-called trace curve (resp. the reduced trace curve) we define a rational map from the Hurwitz space of admissible covers of genus g=2k and degree d=k+1 to a moduli…

We compute the Chow motive and the Chow groups with rational coefficients of the Hilbert scheme of points on a smooth algebraic surface

In this paper we shall generalize the chamber structure of polarizations defined by Qin, and as an application we shall compute the Picard groups of moduli spaces of stable sheaves on a non-rational ruled surface.

We discuss various connections between ideal classes, divisors, Picard and Chow groups of one-dimensional noetherian domains. As a result of these, we give a method to compute Chow groups of orders in global fields and show that there are…