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Flips for 3-folds and 4-folds$
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Alessio Corti

Print publication date: 2007

Print ISBN-13: 9780198570615

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198570615.001.0001

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Extension theorems and the existence of flips

Extension theorems and the existence of flips

(p.76) 5 Extension theorems and the existence of flips
Flips for 3-folds and 4-folds

Christopher D. Hacon

James McKernan

Oxford University Press

This chapter provides a detailed and self-contained exposition of Hacon and McKernan's construction of pl flips in dimension n assuming minimal models with scaling in dimension n-1. The construction is based on the key notion of an ‘adjoint algebra’. The chapter contains an introduction to multiplier ideals, and the celebrated lifting lemma is developed from first principles. Key ideas of the minimal model program for real pairs are also developed from the ground up.

Keywords:   Hacon, McKernan, adjoint algebra, multiplier ideal sheaf, real minimal model program, lifting lemma

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