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Hyperelliptic curves with a-number 1 in small characteristic

Author(s): A. Elkin | R. Pries

Journal: Albanian Journal of Mathematics
ISSN 1930-1235

Volume: 1;
Issue: 4;
Start page: 245;
Date: 2007;
Original page

For every g >= 3, we show there exists a hyperelliptic curve ofgenus g with p-rank g - 3 and a-number 1 in characteristic p when p = 3 orp = 5. The method of proof is to show that a generic point of the moduli spaceof hyperelliptic curves of genus 3 and p-rank 0 has a-number 1. When p = 3,we also show that this moduli space is irreducible.
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