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".
The projectivity of the moduli space of stable curves, II: The stacks M...
The projectivity of the moduli space of stable curves, III: The line bundles on M..., and a proof of the projectivity of M... in characteristic 0.
The rationality of some moduli spaces of plane curves
The Singular Points on the Moduli Spaces for Smooth Curves.
The structure of a local embedding and Chern classes of weighted blow-ups
For a proper local embedding between two Deligne-Mumford stacks and , we find, under certain mild conditions, a new (possibly non-separated) Deligne-Mumford stack , with an etale, surjective and universally closed map to the target , and whose fiber product with the image of the local embedding is a finite union of stacks with corresponding etale, surjective and universally closed maps to . Moreover, a natural set of weights on the substacks of allows the construction of a universally closed...
The tautological ring of
We describe the tautological ring of the moduli space of stable -pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.
Theorem of Enrique-Petri Type for a Very Ample Invertible Sheaf on a Curve of Genus Three.
Thetanullwerte on a moduli space of curves and hyperelliptic loci.
Threefolds in P5 with a 3-dimensional family of plane curves.
Torsion in elliptic curves over
Torsion sur des familles de courbes de genre g.
Toward Clemens' Conjecture in Degrees between 10 and 24
1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.We introduce and study...