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arXiv · 1804.00178

The Gieseker-Petri theorem and imposed ramification

Melody Chan·Brian Osserman·Nathan Pflueger
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Abstract

We prove a smoothness result for spaces of linear series with prescribed ramification on twice-marked elliptic curves. In characteristic 0, we then apply the Eisenbud-Harris theory of limit linear series to deduce a new proof of the Gieseker-Petri theorem, along with a generalization to spaces of linear series with prescribed ramification at up to two points. Our main calculation involves the intersection of two Schubert cycles in a Grassmannian associated to almost-transverse flags.

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Melody Chan, Brian Osserman, Nathan Pflueger. 2018-03-31. The Gieseker-Petri theorem and imposed ramification. https://doi.org/10.1112/blms.12273

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