Vol. 318, No. 2, 2022

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Divisors on surfaces isogenous to a product of mixed type with $p_g=0$

Davide Frapporti and Kyoung-Seog Lee

Vol. 318 (2022), No. 2, 233–247
Abstract

We study effective, nef and semiample cones of surfaces isogenous to a product of mixed type with pg = 0. In particular, we prove that all reducible fake quadrics are Mori dream surfaces.

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Keywords
Mori dream space, surface of general type with $p_g=0$, effective cone, nef cone, semiample cone, Cox ring, surface isogenous to a product of mixed type
Mathematical Subject Classification
Primary: 14E30, 14J29, 14J50
Secondary: 14H37, 14L30, 14Q10
Supplementary material

Magma code supporting the proofs

Milestones
Received: 28 August 2020
Revised: 11 October 2021
Accepted: 2 January 2022
Published: 20 August 2022
Authors
Davide Frapporti
Mathematisches Institut
University of Bayreuth
Lehrstuhl Mathematik VIII
Bayreuth
Germany
Kyoung-Seog Lee
Center for Geometry and Physics
Institute for Basic Science
Pohang
South Korea
Institute of the Mathematical Sciences of the Americas
University of Miami
Coral Gables, FL
USA