Polarized surfaces of \(\Delta\)-genus 3 and degree 5
type: Item
instance of: scholarly article
title: Polarized surfaces of \(\Delta\)-genus 3 and degree 5
zbMATH Open document ID: 0767.14015
author: Masanori Yoshioka
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1993-06-17T00:00:00Z
review text: We try to classify those polarized surfaces \((M,L)\) of \(\Delta\)-genus 3 and degree 5, for which the linear system \(| L|\) has finite base locus and defines a non-birational rational map. Then the surface obtained by blowing up a point of \(M\) is a double covering of a desingularization of a quadric surface. Moreover, we divide these surfaces into four types according to the shape of the fiber containing the exceptional curve. Three of them are fiber spaces over the projective line and the other one is an irrational ruled surface. Conversely, we show the existence of polarized surfaces in each of the four types.
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14J10
zbMATH DE Number: 203565
zbMATH Keywords: \(\Delta\)-genus
zbMATH Keywords: polarized surfaces
zbMATH Keywords: linear system
zbMATH Keywords: finite base locus
zbMATH Keywords: rational map
zbMATH Keywords: desingularization of a quadric surface
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227253
OpenAlex ID: W2030612704
cites work: Q4123438
cites work: On hyperelliptic polarized varieties
cites work: On the structure of polarized manifolds with total deficiency one. III
cites work: Polarized manifolds of degree three and \(\Delta\)-genus two
cites work: Q3995221
cites work: Q4143433
cites work: On deformations of quintic surfaces
DOI: 10.2748/TMJ/1178227253
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description: scientific article; zbMATH DE number 203565