\(\mathfrak{S}_5\)-equivariant syzygies for the del Pezzo surface of degree 5
type: Item
instance of: scholarly article
title: \(\mathfrak{S}_5\)-equivariant syzygies for the del Pezzo surface of degree 5
zbMATH Open document ID: 1469.13023
author: Fabrizio Catanese
author: Ingrid Bauer
publication date: 2021-05-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1812.10715
review text: The del Pezzo surface \(Y\) of degree \(5\) is a smooth nondegenerate in \(\mathbb{P}^5\), which is obtained as the blowup of the project plane in \(4\) points of which no three are collinear. Its automorphism group is the symmetric group \(\mathfrak{S}_5\). The authors give explicitly a \(6 \times 6\) antisymmetric matrix whose \(4 \times 4\)-Pfaffians are the canonical \(\mathfrak{S}_5\)-invariant Pfaffian equations of \(Y\)(Theorem 1.1). Also, the authors give concrete geometric descriptions of the irreducible representations of \(\mathfrak{S}_5\)(Section 3). Finally, the authors show that \(\mathfrak{S}_5\)-invariant equations for the embedding of \(Y\) inside \((\mathbb{P}^1)^5\) have the same Hilbert resolution as for the del Pezzo surface of degree 4 (Theorem 5.2).
reviewed by: Ramakrishna Nanduri
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14J26
Mathematics Subject Classification ID: 14Q10
Mathematics Subject Classification ID: 16E05
Mathematics Subject Classification ID: 20B30
zbMATH DE Number: 7343254
zbMATH Keywords: del Pezzo surface
zbMATH Keywords: Pfaffian equations
zbMATH Keywords: icosahedral symmetry
MaRDI profile type: Publication
OpenAlex ID: W3007879933
arXiv ID: 1812.10715
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DOI: 10.1007/S12215-020-00483-9
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article