Classification of reducible plane curves
type: Item
instance of: scholarly article
title: Classification of reducible plane curves
zbMATH Open document ID: 0668.14025
author: Shigeru Iitaka
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Here it is studied the birational geometry (which is part of ``Iitaka's program'') of a pair (S,C) with S smooth complete rational surface and \(C\subset S\) is a curve with 2 irreducible components. In particular it is proved that if \(S={\mathbb{P}}^ 2 \) C is transformed by a Cremona transformation into the union of two lines if and only if \(h^ 0(S,[2K_ S+2C])=0\).
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14E07
zbMATH DE Number: 4093644
zbMATH Keywords: logarithmic Kodaira dimension
zbMATH Keywords: reducible curve
zbMATH Keywords: birational geometry
zbMATH Keywords: Iitaka's program
zbMATH Keywords: complete rational surface
zbMATH Keywords: Cremona transformation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270133982
OpenAlex ID: W2014154298
DOI: 10.3836/TJM/1270133982
description: scientific article; zbMATH DE number 4093644