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Anti-pluricanonical systems on Fano varieties

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Birkar, Caucher 

Abstract

In this paper, we study the linear systems |−mKX| on Fano varieties X with klt singularities. In a given dimension d, we prove |−mKX| is non-empty and contains an element with "good singularities" for some natural number m depending only on d; if in addition X is ϵ-lc for some ϵ>0, then we show that we can choose m depending only on d and ϵ so that |−mKX| defines a birational map. Further, we prove Shokurov's conjecture on boundedness of complements, and show that certain classes of Fano varieties form bounded families.

Description

Keywords

math.AG, math.AG, 14J45, 14E30, 14C20, 14E05

Journal Title

Annals of Mathematics

Conference Name

Journal ISSN

0003-486X
1939-8980

Volume Title

190

Publisher

Princeton University Press

Rights

All rights reserved