Instanton bundles vs Ulrich bundles on projective spaces
type: Item
instance of: scholarly article
title: Instanton bundles vs Ulrich bundles on projective spaces
zbMATH Open document ID: 1469.14091
author: Laura Costa
author: Rosa M. Miró-Roig
published in: Beiträge zur Algebra und Geometrie
publication date: 2021-05-31T00:00:00Z
review text: Ulrich bundles have been an object of interest in algebra geometry in recent times, being the geometric counterpart of a kind of Maximally Cohen-Macaulay modules with extremal properties. In [J. Am. Math. Soc. 16, No. 3, 537--575, appendix 576--579 (2003; Zbl 1069.14019)], \textit{D. Eisenbud} and \textit{F.-O. Schreyer} raised the question whether any projective variety supports Ulrich sheaves. This paper contributes to this question for the case of the Veronese threefold \(V=(\mathbb{P}^3,\mathcal{O}_{\mathbb{P}^3}(d))\). In order to do it, the authors relate Ulrich bundles with the well-studied family of instanton bundles on \(\mathbb{P}^3\). In particular, they show there exists a correspondence between Ulrich bundles on \(V\) and instanton bundles with natural cohomology and quantum number \(r(d^2-1)/6\). This relation prompts them to conjecture that an Ulrich bundle on \(V\) of rank \(r\) exists if and only if \(r(d^2-1)\) is divisible by \(6\). They solve the conjecture for many values of \((d,r)\).
reviewed by: Joan Pons-Llopis
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14F06
zbMATH DE Number: 7352562
zbMATH Keywords: vector bundles
zbMATH Keywords: Ulrich bundles
zbMATH Keywords: instanton bundles
zbMATH Keywords: Veronese 3-fold
MaRDI profile type: Publication
full work available at URL: s13366-020-00506-7
OpenAlex ID: W3035872352
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DOI: 10.1007/S13366-020-00506-7
description: scientific article; zbMATH DE number 7352562