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Asymptotic syzygies and higher order embeddings

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 نشر من قبل Daniele Agostini
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Daniele Agostini




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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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