相关论文: Quelques remarques sur le champ des courbes hypere…

Let $C$ be a hyperelliptic curve defined over $\mathbb{Q}$, whose Weierstrass points are defined over extensions of $\mathbb{Q}$ of degree at most three, and at least one of them is rational. Generalizing a result of R. Soleng (in the case…

Each finite dimensional irreducible rational representation V of the symplectic group Sp_{2g} determines a generically defined local system \V over the moduli space M_g of genus g smooth projective curves. We study H^2(M_g;\V) and the mixed…

There is a canonical isomorphism between the coarse moduli spaces of somooth hyperelliptic curves of genus g and binary forms of degree 2g+2 with nonzero discriminant. In this paper, we study the extension of this isomorphism to the…

If G is a complex semisimple algebraic group, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant GxG-compactifications which possess a unique closed orbit and which arise in a…

This paper determines the normal forms of hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 0 < g< 9. We also show that every hyperelliptic supersingular curve of genus 9 over F has…

Let E be the supersingular elliptic curve defined over k, the algebraic closure of the finite field with two elements, which is unique up to k-isomorphism. Denote by 0 its identity element and let C be the quotient of E-{0} under the action…

Let $C$ be a smooth projective curve of genus $g\geq 4$ over the complex numbers and ${\cal SU}^s_C(r,d)$ be the moduli space of stable vector bundles of rank $r$ with a fixed determinant of degree $d$. In the projectivized cotangent space…

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.

This paper is about the family of smooth quartic surfaces $X \subset \mathbb{P}^3$ that are invariant under the Heisenberg group $H_{2,2}$. For a very general such surface $X$, we show that the Picard number of $X$ is 16 and determine its…

We study maximal families W of the Hilbert scheme, H(d,g)_{sc}, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth component of…

We use Harer's stability theorem to give another proof of his fundamental theorem: The rank of the Picard group of the moduli space of smooth projective curves of genus g > 2 equals one.

The main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves. We compute their Picard groups, giving explicit description of the generators. We get an application to the…

We investigate the universal Jacobian of degree n line bundles over the Hurwitz stack of double covers of P^1 by a curve of genus g. Our main results are: the construction of a smooth, irreducible, universally closed (but not separated)…

Let $\mathscr{J}^d_g \to \mathscr{M}_g$ be the universal Picard stack parametrizing degree $d$ line bundles on genus $g$ curves, and let $\mathscr{J}^d_{2,g}$ be its restriction to locus of hyperelliptic curves $\mathscr{H}_{2,g} \subset…

We determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne-Mumford compactification, over the field of complex numbers.

The aim of the present paper is to study the (abstract) Picard group and the Picard group scheme of the moduli stack of stable pointed curves over an arbitrary scheme. As a byproduct, we compute the Picard groups of the moduli stack of…

Let G be a complex semi-simple group, and X a compact Riemann surface. The moduli space of principal G-bundles on X, and in particular the holomorphic line bundles on this space and their global sections, play an important role in the…

Let S be a site. We introduce the 2-category of biextensions of strictly commutative Picard S-stacks. We define the pull-back, the push-down, and the sum of such biextensions and we compute their homological interpretation: if P,Q and G are…

We find a closed formula for the number $\operatorname{hyp}(g)$ of hyperelliptic curves of genus $g$ over a finite field $k=\mathbb{F}_q$ of odd characteristic. These numbers $\operatorname{hyp}(g)$ are expressed as a polynomial in $q$ with…

Consider a hyperelliptic curve of genus $g$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $2g+2$ Weierstrass points. We prove some general properties of the stable reduction of this…