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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 3, Pages 54–74 (Mi faa3119)  

This article is cited in 1 scientific paper (total in 1 paper)

Syzygy Algebras for Segre Embeddings

I. V. Netayab

a Independent University of Moscow
b Mathematical Department of Higher School of Economics

Abstract: We describe the syzygy spaces for the Segre embedding $\mathbb{P}(U)\times\mathbb{P}(V)\subset\mathbb{P}(U\otimes V)$ in terms of representations of $\operatorname{GL}(U)\times\operatorname{GL}(V)$ and construct the minimal resolutions of the sheaves $\mathcal{O}_{\mathbb{P}(U)\times\mathbb{P}(V)}(a,b)$ in $D(\mathbb{P}(U\otimes V))$ for $a\ge-\dim(U)$ and $b\ge-\dim(V)$. We also prove a property of multiplication in syzygy spaces of the Segre embedding.

Keywords: syzygy algebra, Koszul cohomology, representations of $\operatorname{GL}$, Segre embedding, derived category of coherent sheaves.

DOI: https://doi.org/10.4213/faa3119

Full text: PDF file (275 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:3, 210–226

Bibliographic databases:

UDC: 512.815.2+512.664.1+512.723
Received: 12.12.2011

Citation: I. V. Netay, “Syzygy Algebras for Segre Embeddings”, Funktsional. Anal. i Prilozhen., 47:3 (2013), 54–74; Funct. Anal. Appl., 47:3 (2013), 210–226

Citation in format AMSBIB
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\pages 54--74
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    This publication is cited in the following articles:
    1. I. V. Netay, “Syzygies of quadratic Veronese embedding”, Sb. Math., 208:2 (2017), 200–222  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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