Monomial equimultiple curves in positive characteristic

Projective Monomial Curves in P

The Hodge-Arakelov Theory of Elliptic Curves in Positive Characteristic

The purpose of this paper is to study the Hodge-Arakelov theory of elliptic curves (cf. [Mzk1-4]) in positive characteristic. The first two §’s (§1,2) are devoted to studying the relationship of the Frobenius and Verschiebung morphisms of an elliptic curve in positive characteristic to the Hodge-Arakelov theory of elliptic curves. We begin by deriving a “Verschiebung-Theoretic Analogue of the H...

Automorphisms of Hyperelliptic Modular Curves X0(n) in Positive Characteristic

We study the automorphism groups of the reduction X0(N)× F̄p of a modular curve X0(N) over primes p ∤ N .

Curves Whose Secant Degree Is One in Positive Characteristic

Here we study (in positive characteristic) integral curves X ⊂ Pr with secant degree one, i.e., for which a general P ∈ Seck−1(X) is in a unique k-secant (k − 1)-dimensional linear subspace.

Moduli of Vector Bundles on Curves in Positive Characteristic

Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli space of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 with determinant equal to a theta characteristic whose Frobenius pull-back is not sta...