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Super-rigid affine Fano varieties

Part of: Cycles and subschemes Birational geometry Affine geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  17 October 2018

Ivan Cheltsov ,
Adrien Dubouloz  and
Jihun Park
Ivan Cheltsov
Affiliation:
School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK Laboratory of Algebraic Geometry, National Research University Higher School of Economics, 6 Usacheva street, Moscow, 117312, Russia email [email protected]
Adrien Dubouloz
Affiliation:
IMB UMR5584, CNRS, Université Bourgogne Franche-Comté F-21000 Dijon, France email [email protected]
Jihun Park
Affiliation:
Center for Geometry and Physics, Institute for Basic Science (IBS), 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, 37673, Korea Department of Mathematics, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, 37673, Korea email [email protected]
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Abstract

We study a wide class of affine varieties, which we call affine Fano varieties. By analogy with birationally super-rigid Fano varieties, we define super-rigidity for affine Fano varieties, and provide many examples and non-examples of super-rigid affine Fano varieties.

Keywords

A1 -cylinderaffine Fano variety𝛼-invariantautomorphismbirational automorphismdel Pezzo surfaceFano varietyfinite quotient of affine spaceGa -actionlog Noether–Fano inequalitypolar cylinderpurely log terminalsuper-rigidity

MSC classification

Primary: 14E07: Birational automorphisms, Cremona group and generalizations 14J45: Fano varieties 14J50: Automorphisms of surfaces and higher-dimensional varieties 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 14R20: Group actions on affine varieties 14R25: Affine fibrations
Secondary: 14C20: Divisors, linear systems, invertible sheaves 14E05: Rational and birational maps 14J17: Singularities 14J70: Hypersurfaces
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 11 , November 2018 , pp. 2462 - 2484
Copyright
© The Authors 2018 

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