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On Intrinsic Quadrics

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

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

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

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Footnotes

Supported by the Carl-Zeiss-Stiftung.

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