Imperial College London
Alternate

Professor Paolo Cascini

Faculty of Natural Sciences, Department of Mathematics

Head of Pure Mathematics Section/Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8861p.cascini

 
 
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Location

 

676Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Cascini:2020:10.1007/s00208-019-01877-6,
author = {Cascini, P and Meng, S and Zhang, D-Q},
doi = {10.1007/s00208-019-01877-6},
journal = {Mathematische Annalen},
pages = {637--665},
title = {Polarized endomorphisms of normal projective threefolds in arbitrarycharacteristic},
url = {http://dx.doi.org/10.1007/s00208-019-01877-6},
volume = {378},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Let X be a projective variety over an algebraically closed field k of arbitrary characteristic p≥0. A surjective endomorphism f of X is q-polarized if f∗H∼qH for some ample Cartier divisor H and integer q>1. Suppose f is separable and X is Q-Gorenstein and normal. We show that the anti-canonical divisor −KX is numerically equivalent to an effective Q-Cartier divisor, strengthening slightly the conclusion of Boucksom, de Fernex and Favre (Duke Math J 161(8):1455–1520, 2012, Theorem C) and also covering singular varieties over an algebraically closed field of arbitrary characteristic. Suppose f is separable and X is normal. We show that the Albanese morphism of X is an algebraic fibre space and f induces polarized endomorphisms on the Albanese and also the Picard variety of X, and KX being pseudo-effective and Q-Cartier means being a torsion Q-divisor. Let fGal:X¯¯¯¯→X be the Galois closure of f. We show that if p>5 and co-prime to degfGal then one can run the minimal model program (MMP) f-equivariantly, after replacing f by a positive power, for a mildly singular threefold X and reach a variety Y with torsion canonical divisor (and also with Y being a quasi-étale quotient of an abelian variety when dim(Y)≤2). Along the way, we show that a power of f acts as a scalar multiplication on the Neron-Severi group of X (modulo torsion) when X is a smooth and rationally chain connected projective variety of dimension at most three.
AU  - Cascini,P
AU  - Meng,S
AU  - Zhang,D-Q
DO  - 10.1007/s00208-019-01877-6
EP  - 665
PY  - 2020///
SN  - 0025-5831
SP  - 637
TI  - Polarized endomorphisms of normal projective threefolds in arbitrarycharacteristic
T2  - Mathematische Annalen
UR  - http://dx.doi.org/10.1007/s00208-019-01877-6
UR  - http://arxiv.org/abs/1710.01903v2
UR  - http://hdl.handle.net/10044/1/93841
VL  - 378
ER  -
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