Conic bundles that are not birational to numerical Calabi-Yau pairs

János Kollár

Conic bundles that are not birational to numerical Calabi-Yau pairs

János Kollár

Mathematics

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

5 Scopus citations

Abstract

Let X be a general conic bundle over P² with branch curve of degree at least 19. We prove that there is no normal projective variety Y that is birational to X and such that some multiple of its anticanonical divisor is effective.

Original language	English (US)
Pages (from-to)	1-14
Number of pages	14
Journal	Epijournal de Geometrie Algebrique
Volume	1
State	Published - 2017

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Keywords

Birational equivalence
Calabi-Yau variety
Conic bundle
Rationally connected variety

Cite this

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title = "Conic bundles that are not birational to numerical Calabi-Yau pairs",

abstract = "Let X be a general conic bundle over P2 with branch curve of degree at least 19. We prove that there is no normal projective variety Y that is birational to X and such that some multiple of its anticanonical divisor is effective.",

keywords = "Birational equivalence, Calabi-Yau variety, Conic bundle, Rationally connected variety",

author = "J{\'a}nos Koll{\'a}r",

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year = "2017",

language = "English (US)",

volume = "1",

pages = "1--14",

journal = "Epijournal de Geometrie Algebrique",

issn = "2491-6765",

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T1 - Conic bundles that are not birational to numerical Calabi-Yau pairs

AU - Kollár, János

N1 - Publisher Copyright: © by the author(s)

PY - 2017

Y1 - 2017

N2 - Let X be a general conic bundle over P2 with branch curve of degree at least 19. We prove that there is no normal projective variety Y that is birational to X and such that some multiple of its anticanonical divisor is effective.

AB - Let X be a general conic bundle over P2 with branch curve of degree at least 19. We prove that there is no normal projective variety Y that is birational to X and such that some multiple of its anticanonical divisor is effective.

KW - Birational equivalence

KW - Calabi-Yau variety

KW - Conic bundle

KW - Rationally connected variety

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AN - SCOPUS:85069570358

SN - 2491-6765

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JO - Epijournal de Geometrie Algebrique

JF - Epijournal de Geometrie Algebrique

ER -

Conic bundles that are not birational to numerical Calabi-Yau pairs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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