On the crepant blowing-ups of canonical singularities and its application to degenerations of surfaces
type: Item
instance of: scholarly article
title: On the crepant blowing-ups of canonical singularities and its application to degenerations of surfaces
zbMATH Open document ID: 0605.14012
author: Yujiro Kawamata
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: This note gives a sketch of the proof of the following theorem: \(Let\quad X\) be a 3-dimensional normal complex algebraic variety with at most canonical singularities. Then the ring \(\oplus_{m\geq 0}{\mathcal O}_ X(m.D)\quad is\) finitely generated, where D is a Weil divisor on X. This result is then applied to prove the existence of minimal models for on-parameter-families of surfaces of non-negative Kodaira-dimension whose degenerate members are reduced and have only simple normal crossings.
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14J10
zbMATH DE Number: 3977140
zbMATH Keywords: blowing-ups
zbMATH Keywords: threefold
zbMATH Keywords: canonical singularities
zbMATH Keywords: minimal models for on- parameter-families of surfaces
MaRDI profile type: Publication
full work available at URL: pjaa.62.104
OpenAlex ID: W2044950893
cites work: Zariski decomposition of divisors on algebraic varieties
cites work: Q3803246
cites work: Q3825176
cites work: Q3794299
cites work: Q3222980
cites work: Q4731280
cites work: The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface
DOI: 10.3792/PJAA.62.104
description: scientific article; zbMATH DE number 3977140