On nondegeneracy of curves

Details On nondegeneracy of curves On nondegeneracy of curves

2008-02-04

arxiv.org/abs/0802.0420v2

Mathematics

Algebraic Geometry

Scientific paper

A curve is called nondegenerate if it can be modeled by a Laurent polynomial
that is nondegenerate with respect to its Newton polytope. We show that up to
genus 4, every curve is nondegenerate. We also prove that the locus of
nondegenerate curves inside the moduli space of curves of fixed genus g > 1 is
min(2g+1,3g-3)-dimensional, except in case g=7 where it is 16-dimensional.

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