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On Intrinsic Quadrics

Part of: Cycles and subschemes Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  09 January 2019

Anne Fahrner  and
Jürgen Hausen
Anne Fahrner
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany Email: fahrner@math.uni-tuebingen.dejuergen.hausen@uni-tuebingen.de
Jürgen Hausen
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany Email: fahrner@math.uni-tuebingen.dejuergen.hausen@uni-tuebingen.de
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Abstract

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An intrinsic quadric is a normal projective variety with a Cox ring defined by a single quadratic relation. We provide explicit descriptions of these varieties in the smooth case for small Picard numbers. As applications, we figure out in this setting the Fano examples and (affirmatively) test Fujita’s freeness conjecture.

Keywords

Fano varietyCox ringMori dream spaceintrinsic quadric

MSC classification

Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14J10: Families, moduli, classification 14J45: Fano varieties

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 1 , February 2020 , pp. 145 - 181
Copyright
© Canadian Mathematical Society 2018 

Footnotes

Supported by the Carl-Zeiss-Stiftung.

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