Birational maps between Calabi-Yau manifolds associated to webs of quadrics

Mateusz Michalek

doi:10.1016/j.jalgebra.2012.07.019

Birational maps between Calabi-Yau manifolds associated to webs of quadrics

Mateusz Michalek^*

^*Corresponding author for this work

Not published at Aalto University

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

Abstract

We consider two varieties associated to a web of quadrics W in P-7. One is the base locus and the second one is the double cover of P-3 branched along the determinant surface of W. We show that small resolutions of these varieties are Calabi-Yau manifolds. We compute their Betti numbers and show that they are not birational in the generic case. The main result states that if the base locus of W contains a plane then in the generic case the two varieties are birational. (C) 2012 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	186-197
Number of pages	12
Journal	JOURNAL OF ALGEBRA
Volume	370
DOIs	https://doi.org/10.1016/j.jalgebra.2012.07.019
Publication status	Published - 15 Nov 2012
MoE publication type	A1 Journal article-refereed

Keywords

Webs of quadrics
Calabi-Yau manifolds

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10.1016/j.jalgebra.2012.07.019

Cite this

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title = "Birational maps between Calabi-Yau manifolds associated to webs of quadrics",

abstract = "We consider two varieties associated to a web of quadrics W in P-7. One is the base locus and the second one is the double cover of P-3 branched along the determinant surface of W. We show that small resolutions of these varieties are Calabi-Yau manifolds. We compute their Betti numbers and show that they are not birational in the generic case. The main result states that if the base locus of W contains a plane then in the generic case the two varieties are birational. (C) 2012 Elsevier Inc. All rights reserved.",

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AU - Michalek, Mateusz

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N2 - We consider two varieties associated to a web of quadrics W in P-7. One is the base locus and the second one is the double cover of P-3 branched along the determinant surface of W. We show that small resolutions of these varieties are Calabi-Yau manifolds. We compute their Betti numbers and show that they are not birational in the generic case. The main result states that if the base locus of W contains a plane then in the generic case the two varieties are birational. (C) 2012 Elsevier Inc. All rights reserved.

AB - We consider two varieties associated to a web of quadrics W in P-7. One is the base locus and the second one is the double cover of P-3 branched along the determinant surface of W. We show that small resolutions of these varieties are Calabi-Yau manifolds. We compute their Betti numbers and show that they are not birational in the generic case. The main result states that if the base locus of W contains a plane then in the generic case the two varieties are birational. (C) 2012 Elsevier Inc. All rights reserved.

KW - Webs of quadrics

KW - Calabi-Yau manifolds

U2 - 10.1016/j.jalgebra.2012.07.019

DO - 10.1016/j.jalgebra.2012.07.019

M3 - Article

VL - 370

SP - 186

EP - 197

JO - JOURNAL OF ALGEBRA

JF - JOURNAL OF ALGEBRA

SN - 0021-8693

ER -

Birational maps between Calabi-Yau manifolds associated to webs of quadrics

Abstract

Keywords

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