Spin curves and Scorza quartics

Details Spin curves and Scorza quartics Spin curves and Scorza quartics

2009-04-23

arxiv.org/abs/0904.3590v1

Mathematics

Algebraic Geometry

This is the second part of the division of the paper of arXiv:0801.1760. This is the application part of our method

Scientific paper

In the previous paper, we construct new subvarieties in the varieties of power sums for certain quartic hypersurfaces. In this paper, we show that these quartics coincide with the Scorza quartics of general pairs of trigonal curves and ineffective theta characteristics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartics for any general pairs of curves and ineffective theta characteristics. We also give descriptions of the moduli spaces of trigonal even spin curves. For curves of genus 4, we deepen this description in the next paper.

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