Rational correspondences between moduli spaces of curves defined by Hurwitz spaces

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 space of stable curves. We study the induced map between the divisor class groups of these moduli spaces of curves.Comment: 25 pages, late

The Hodge bundle on Hurwitz spaces

In 2009 Kokotov, Korotkin and Zograf gave a formula for the class of the Hodge bundle on the Hurwitz space of admissible covers of genus g and degree d of the projective line. They gave an analytic proof of it. In this note we give an algebraic proof and an extension of the result.Comment: 8 pages; misprints correcte

Geometry of lines on a cubic fourfold

For a general cubic fourfold $X\subset\mathbb{P}^5$ with Fano scheme of lines $F$, we prove a number of properties of the fibration of genus 4 curves from the universal family of lines $p:I\to X$. We compute the classes of various ramification loci attached to this fibration and use this to compute the class of the locus of triple lines, i.e., the fixed locus $V$ of the Voisin map $\phi:F\dashrightarrow F$, which we prove is a smooth irreducible surface if $X$ is general. In the final two sections, we compute the Hodge numbers of the locus $S\subset F$ of lines of second type and give an upper bound for the degree of irrationality of the Fano scheme of lines of any smooth cubic hypersurface

The rank-one limit of the Fourier-Mukai transform

We give a formula for the specialization of the Fourier-Mukai transform on a semi-abelian variety of torus rank 1.Comment: 15 pages; a sign mistake correcte

Automorphisms of moduli spaces of vector bundles over a curve

Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank r and fixed determinant \Lambda, of degree d. We give a new proof of the fact that the automorphism group of M(r,\Lambda) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, if r divides 2d, also dualization of vector bundles.Comment: 12 page