MORI DREAM SPACES AND-HOMOLOGY QUADRICS

Paolo Cascini; Fabrizio Catanese; Yifan Chen; Jonghae Keum

doi:10.2140/pjm.2025.339.223

MORI DREAM SPACES AND-HOMOLOGY QUADRICS

Paolo Cascini
, Fabrizio Catanese
, Yifan Chen
, Jonghae Keum

School of Mathematical Sciences

Imperial College London
University of Bayreuth
Korea Institute for Advanced Study

Research output: Contribution to journal › Article › peer-review

Abstract

We show that Shavel-type surfaces are fake \mathbb{Q}-homology quadrics of even type which are not Mori dream surfaces, yet there are infinitely many primes p such that the reduction modulo p is a Mori dream surface. We investigate fake \mathbb{Q}-homology quadrics, first concerning the property of being a Mori dream surface, then trying to determine which families are of even type among the surfaces isogenous to a higher product which are fake \mathbb{Q}-homology quadrics.

Original language	English
Pages (from-to)	223-242
Number of pages	20
Journal	Pacific Journal of Mathematics
Volume	339
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2025.339.223
State	Published - 2025

Keywords

Mori dream space
fake quadric
foliation
group action
homology quadric
surface isogenous to a product
surfaces of general type

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10.2140/pjm.2025.339.223

Cite this

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title = "MORI DREAM SPACES AND-HOMOLOGY QUADRICS",

abstract = "We show that Shavel-type surfaces are fake \textbackslash{}mathbb\{Q\}-homology quadrics of even type which are not Mori dream surfaces, yet there are infinitely many primes p such that the reduction modulo p is a Mori dream surface. We investigate fake \textbackslash{}mathbb\{Q\}-homology quadrics, first concerning the property of being a Mori dream surface, then trying to determine which families are of even type among the surfaces isogenous to a higher product which are fake \textbackslash{}mathbb\{Q\}-homology quadrics.",

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AU - Keum, Jonghae

N1 - Publisher Copyright: © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY) https://creativecommons.org/licenses/by-nc-nd/4.0/. Open Access made possible by subscribing institutions via Subscribe to Open.

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KW - fake quadric

KW - foliation

KW - group action

KW - homology quadric

KW - surface isogenous to a product

KW - surfaces of general type

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ER -

MORI DREAM SPACES AND-HOMOLOGY QUADRICS

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