Irregularity of quintic surfaces of general type
type: Item
instance of: scholarly article
title: Irregularity of quintic surfaces of general type
zbMATH Open document ID: 0873.14034
author: Yumiko Umezu
published in: Tokyo Journal of Mathematics
publication date: 1994-09-28T00:00:00Z
review text: In this paper we prove the following theorem. Let \(X\) be a normal quintic surface in \(\mathbb{P}^3\) and let \(\widetilde X\) be a resolution of \(X\). If \(\widetilde X\) is of general type, then its irregularity vanishes. This result was proved also by \textit{J.-G. Yang} [Trans. Am. Math. Soc. 295, 431-473 (1986; Zbl 0596.14029)] as a corollary of a classification of singularities on \(X\). To the contrary our proof is direct. We study invariants of \(\widetilde X\) and then find a contradiction if the irregularity is not zero. Our method can be also applied to other surfaces of lower degree. In fact, we apply this method to prove the nonexistence of normal quintic surfaces which are birationally equivalent to an abelian or a hyperelliptic surface [\textit{I. Nakamura} and \textit{Y. Umezu}, ``Nonexistence of normal quintic abelian surfaces in \(\mathbb{P}^3\)'', Tokyo J. Math. 18, No. 2, 369-382 (1995)].
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 14E15
zbMATH DE Number: 645694
zbMATH Keywords: quintic surfaces of general type
zbMATH Keywords: resolution of singularities
zbMATH Keywords: irregularity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270128196
OpenAlex ID: W2012648828
DOI: 10.3836/TJM/1270128196
description: scientific article; zbMATH DE number 645694