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arXiv · 1706.03508

Asymptotic syzygies and higher order embeddings

Daniele Agostini
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Abstract

We show that vanishing of asymptotic p-th syzygies implies p-very ampleness for line bundles on arbitrary projective schemes. For smooth surfaces we prove that the converse holds when p is small, by studying the Bridgeland-King-Reid-Haiman correspondence for tautological bundles on the Hilbert scheme of points. This extends previous results of Ein-Lazarsfeld, Ein-Lazarsfeld-Yang and gives a partial answer to some of their questions. As an application of our results, we show how to use syzygies to bound the irrationality of a variety.

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Daniele Agostini. 2017-06-12. Asymptotic syzygies and higher order embeddings. https://arxiv.org/abs/1706.03508

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