Related papers: Abel maps of Gorenstein curves

Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X…

We generalize Abel's classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold $M^d \subset X^n$ in a compact oriented Riemannian $n$--manifold, or more generally for any $d$--cycle $Z$ relative…

This survey article discusses some results on the structure of families f:V-->U of n-dimensional manifolds over quasi-projective curves U, with semistable reduction over a compactification Y of U. We improve the Arakelov inequality for the…

Given a family $X/B$ of nodal curves, we construct canonically and compatibly with base-change, via an explicit blow-up of the Cartesian product $X^r/B$, a family $W^r(X/B)$ parametrizing length-$r$ subschemes of fibres of $X/B$ (plus some…

Given a genus two curve $X: y^2 = x^5 + a x^3 + b x^2 + c x + d$, we give an explicit parametrization of all other such curves $Y$ with a specified symplectic isomorphism on three-torsion of Jacobians $\mbox{Jac}(X)[3] \cong…

Let $X$ be a curve of genus $g\geq 2$ over a number field $F$ of degree $d = [F:Q]$. The conjectural existence of a uniform bound $N(g,d)$ on the number $\#X(F)$ of $F$-rational points of $X$ is an outstanding open problem in arithmetic…

Let $S$ be a connected Dedekind scheme and $X$ an $S$-scheme provided with a section $x$. We prove that the morphism of fundamental group schemes $\pi_1(X,x)^{ab}\to \pi_1(\mathbf{Alb}_{X/S},0_{\mathbf{Alb}_{X/S}})$ induced by the canonical…

In this survey article we want to discuss a way of constructing arithmetically Gorenstein varieties of high codimension. Consider kernel sheaves B_G of general, generically surjective morphisms G between decomposable bundles on P^n. The…

In this paper, we are concerned with the computation of the $p$-rank and $a$-number of singular curves and their smooth model. We consider a pair $X, X'$ of proper curves over an algebraically closed field $k$ of characteristic $p$, where…

We investigate the "natural" locus of definition of Abel-Jacobi maps. In particular, we show that, for a proper, geometrically reduced curve C -- not necessarily smooth -- the Abel-Jacobi map from the smooth locus C^{sm} into the Jacobian…

For a curve $X$ over a $p$-adic field $k$, using the class field theory of $X$ due to S. Bloch and S. Saito we study the abelian geometric fundamental group $\pi_1^{\mathrm{ab}}(X)^{\mathrm{geo}}$ of $X$. In particular, it is investigated a…

We define the cohomological Hall algebra ${AHA}_{Higgs(X)}$ of the ($2$-dimensional) Calabi-Yau category of Higgs sheaves on a smooth projective curve $X$, as well as its nilpotent and semistable variants, in the context of an arbitrary…

We show that algebraic equivalence of images of stable maps of curves lifts to deformation equivalence of the stable maps. The main applications concern $A_1(X)$, the group of 1-cycles modulo algebraic equivalence, for smooth, separably…

We show that regular semisimple Hessenberg varieties can have moduli. To be precise, suppose $X$ is a regular semisimple Hessenberg variety of codimension $1$ in the flag variety $G/B$, where $G$ is a simple algebraic group of rank $r$ over…

On a threefold with trivial canonical bundle, Kuranishi theory gives an algebro-geometry construction of the (local analytic) Hilbert scheme of curves at a smooth holomorphic curve as a gradient scheme, that is, the zero-scheme of the…

In this paper, we describe an algorithm that, for a smooth connected curve $X$ over a field $k$ with normal completion having arithmetic genus $p_a(X)$, a finite locally constant sheaf $\mathcal A$ on $X_{et}$ of abelian groups of torsion…

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $\alpha$ a class of…

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…

We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with…

Let G be a connected reductive algebraic group acting on a scheme X. Let R(G) denote the representation ring of G, and let I be the ideal in R(G) of virtual representations of rank 0. Let G(X) (resp. G(G,X)) denote the Grothendieck group of…