Displaying similar documents to “Basics on families of hyperelliptic curves”

Curves on a double surface.

Scott Nollet, Enrico Schlesinger (2003)

Collectanea Mathematica

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Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes...

Hurwitz spaces of genus 2 covers of an elliptic curve.

Ernst Kani (2003)

Collectanea Mathematica

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Let E be an elliptic curve over a field K of characteristic not equal to 2 and let N > 1 be an integer prime to char(K). The purpose of this paper is to construct the (two-dimensional) Hurwitz moduli space H (E/K,N,2) which classifies genus 2 covers of E of degree N and to show that it is closely related to the modular curve X(N) which parametrizes elliptic curves with level-N-structure. More precisely, we introduce the notion of a normalized genus 2 cover of E/K and show that...

Curves with only triple ramification

Stefan Schröer (2003)

Annales de l'Institut Fourier

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We show that the set of smooth curves of genus g ≥ 0 admitting a branched covering X → ℙ 1 with only triple ramification points is of dimension at least max ( 2 g - 3 , g ) . In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.