A Cuspidal Class Number Formula for the Modular Curves X1(N).
A descendent relation in genus 2
A descent map for curves with totally degenerate semi-stable reduction
Let be a local field of residue characteristic . Let be a curve over whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- rational torsion subgroup on the Jacobian of . We also determine divisibility of line bundles on , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of .
A Diophantine problem on algebraic curves over function fields of positive characteristic
A diophantine system.
A duality result for moduli spaces of semistable sheaves supported on projective curves
A duality theorem for divisors on certain algebraic curves
A dynamical system connected with inhomogeneous 6-vertex model
A factorization theorem for the polar of a curve with two branches
A Family of Abelian Surfaces and Curves of Genus Four.
A family of K3 surfaces and ... (3).
A few remarks about the variety of irreducible plane curves of given degree and genus
A finiteness theorem for the symmetric square of an elliptic curve.
A footnote to the Poincaré complete reducibility theorem.
Poincaré's work on the reduction of Abelian integrals contains implicitly an algorithm for the expression of a theta function as a sum of products of theta functions of fewer variables in the presence of reduction. The aim of this paper is to give explicit formulations and reasonably complete proofs of Poincaré's results.
A formula for the Cartier operator on plane algebraic curves.
A functional equation originating from elliptic curves.
A fundamental domain for the Fermat curves and their quotients.
A GAP package for braid orbit computation and applications.
A generalization of the Chowla-Selberg formula.
A generating function for fatgraphs