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https://doi.org/10.1007/s00208-019-01877-6
DC Field | Value | |
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dc.title | Polarized endomorphisms of normal projective threefolds in arbitrary characteristic | |
dc.contributor.author | Cascini, Paolo | |
dc.contributor.author | Meng, Sheng | |
dc.contributor.author | Zhang, De-Qi | |
dc.date.accessioned | 2022-11-17T01:08:11Z | |
dc.date.available | 2022-11-17T01:08:11Z | |
dc.date.issued | 2020-10-01 | |
dc.identifier.citation | Cascini, Paolo, Meng, Sheng, Zhang, De-Qi (2020-10-01). Polarized endomorphisms of normal projective threefolds in arbitrary characteristic. MATHEMATISCHE ANNALEN 378 (1-Feb) : 637-665. ScholarBank@NUS Repository. https://doi.org/10.1007/s00208-019-01877-6 | |
dc.identifier.issn | 0025-5831 | |
dc.identifier.issn | 1432-1807 | |
dc.identifier.uri | https://scholarbank.nus.edu.sg/handle/10635/234646 | |
dc.description.abstract | 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 deg fGal 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. | |
dc.language.iso | en | |
dc.publisher | SPRINGER HEIDELBERG | |
dc.source | Elements | |
dc.subject | Science & Technology | |
dc.subject | Physical Sciences | |
dc.subject | Mathematics | |
dc.subject | 14H30 | |
dc.subject | 32H50 | |
dc.subject | 14E30 | |
dc.subject | 11G10 | |
dc.subject | 08A35 | |
dc.subject | VARIETIES | |
dc.subject | 3-FOLDS | |
dc.type | Article | |
dc.date.updated | 2022-11-16T08:12:50Z | |
dc.contributor.department | MATHEMATICS | |
dc.description.doi | 10.1007/s00208-019-01877-6 | |
dc.description.sourcetitle | MATHEMATISCHE ANNALEN | |
dc.description.volume | 378 | |
dc.description.issue | 1-Feb | |
dc.description.page | 637-665 | |
dc.published.state | Published | |
Appears in Collections: | Staff Publications Elements |
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