Triple planes with p_g=q=0

We show that general triple planes with genus and irregularity zero belong to at most 12 families, that we call surfaces of type I to XII, and we prove that the corresponding Tschirnhausen bundle is a direct sum of two line bundles in cases I, II, III, whereas it is a rank 2 Steiner bundle in the re...

Full description

Saved in:
Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019-01, Vol.371 (1), p.589-639
Main Authors: Faenzi, Daniele, Polizzi, Francesco, Vallès, Jean
Format: Article
Language:English
Subjects:
Algebraic Geometry
Mathematics
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that general triple planes with genus and irregularity zero belong to at most 12 families, that we call surfaces of type I to XII, and we prove that the corresponding Tschirnhausen bundle is a direct sum of two line bundles in cases I, II, III, whereas it is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit descriptions for surfaces of type I to VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski. Finally, in the last part of the paper we discuss some moduli problems related to our constructions.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7276