The Geometry of the Moduli Space of Curves of Genus 23

Details The Geometry of the Moduli Space of Curves of Genus 23 The Geometry of the Moduli Space of Curves of Genus 23

1999-07-02

arxiv.org/abs/math/9907013v1

Mathematics

Algebraic Geometry

21 pages, Latex

Scientific paper

We prove that the Kodaira dimension of the moduli space M_{23} of curves of genus 23 is at least 2. We also present some evidence for the hypothesis that the Kodaira dimension of the moduli space is actually equal to 2. Note that for g > 23 the moduli space is of general type, while for g\leq 22, Harris and Morrison conjectured that M_g is uniruled. The result on M_{23} is obtained by investigating the relative position of three explicit multicanonical divisors which are of Brill-Noether type.

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