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arXiv · 1504.03756

Invariants of a general branched cover of ${\bf P}^{1}$

Gabriel Bujokas·Anand Patel
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Abstract

We investigate the resolution of a general branched cover $\alpha : C \to {\bf P}^1$ in its relative canonical embedding $C \subset {\bf P} E$. We conjecture that the syzygy bundles appearing in the resolution are balanced for a general cover, provided that the genus is sufficiently large compared to the degree. We prove this for the Casnati-Ekedahl bundle, or "bundle of quadrics" $F$ - the first bundle appearing in the resolution of the ideal of the relative canonical embedding. Furthermore, we prove the conjecture for all syzygy bundles in the resolution when the genus satisfies $g = 1 \mod d$.

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Gabriel Bujokas, Anand Patel. 2015-04-15. Invariants of a general branched cover of ${\bf P}^{1}$. https://arxiv.org/abs/1504.03756

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