The dimension of the Chow variety of curves
The divisor of curves with a vanishing theta-null
The embedding dimension of the formal Moduli space of certain curve singularities.
The Euler characteristic of the moduli space of curves.
The Fibre of the Prym Map in Genus Three.
The fourth tautological group of and relations with the cohomology
We give a complete description of the fourth tautological group of the moduli space of pointed stable curves, , and prove that for it coincides with the cohomology group with rational coefficients. We further give a conjectural upper bound depending on the genus for the degree of new tautological relations.
The geometry of the period mapping on cyclic covers of P1
The Hyperelliptic Locus with Special Reference to Characteristic Two.
The Kodaira dimension of the moduli space of curves of genus ... 23.
The Lefshetz Vanishing Cycles on a Projective Nonsingular Plane Curve.
The line bundles on moduli stacks of principal bundles on a curve.
The maximal rank conjecture for non-special curves in IP3.
The moduli space of curves of genus two covering elliptic curves.
The moduli space of Riemann surfaces is Kähler hyperbolic.
The Moduli Spaces of Vector Bundles over an Algebraic Curve.
The monodromy of Weierstrass points.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The -rank stratification of Artin-Schreier curves
We study a moduli space for Artin-Schreier curves of genus over an algebraically closed field of characteristic . We study the stratification of by -rank into strata of Artin-Schreier curves of genus with -rank exactly . We enumerate the irreducible components of and find their dimensions. As an application, when , we prove that every irreducible component of the moduli space of hyperelliptic -curves with genus and -rank has dimension . We also determine all pairs for...
The Picard group of the moduli of higher spin curves.
The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".