Pullbacks of hyperplane sections for Lagrangian fibrations are primitive

Ljudmila Kamenova; Misha Verbitsky

doi:10.1142/S0219199718500657

Pullbacks of hyperplane sections for Lagrangian fibrations are primitive

Ljudmila Kamenova
, Misha Verbitsky

Mathematics

Université libre de Bruxelles
Higher School of Economics

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

2 Scopus citations

Abstract

Let p: M → B be a Lagrangian fibration on a hyperkähler manifold of maximal holonomy (also known as IHS), and H be the generator of the Picard group of B. Assume that p has no multiple fibers in codimension 1. We prove that p∗(H) is a primitive class on M.

Original language	English
Article number	1850065
Journal	Communications in Contemporary Mathematics
Volume	21
Issue number	8
DOIs	https://doi.org/10.1142/S0219199718500657
State	Published - Dec 1 2019

Keywords

Hyperkähler manifolds
Lagrangian fibrations
SYZ conjecture

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10.1142/S0219199718500657

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title = "Pullbacks of hyperplane sections for Lagrangian fibrations are primitive",

abstract = "Let p: M → B be a Lagrangian fibration on a hyperk{\"a}hler manifold of maximal holonomy (also known as IHS), and H be the generator of the Picard group of B. Assume that p has no multiple fibers in codimension 1. We prove that p∗(H) is a primitive class on M.",

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author = "Ljudmila Kamenova and Misha Verbitsky",

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AU - Verbitsky, Misha

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N2 - Let p: M → B be a Lagrangian fibration on a hyperkähler manifold of maximal holonomy (also known as IHS), and H be the generator of the Picard group of B. Assume that p has no multiple fibers in codimension 1. We prove that p∗(H) is a primitive class on M.

AB - Let p: M → B be a Lagrangian fibration on a hyperkähler manifold of maximal holonomy (also known as IHS), and H be the generator of the Picard group of B. Assume that p has no multiple fibers in codimension 1. We prove that p∗(H) is a primitive class on M.

KW - Hyperkähler manifolds

KW - Lagrangian fibrations

KW - SYZ conjecture

UR - https://www.scopus.com/pages/publications/85056660514

U2 - 10.1142/S0219199718500657

DO - 10.1142/S0219199718500657

M3 - Article

AN - SCOPUS:85056660514

SN - 0219-1997

VL - 21

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 8

M1 - 1850065

ER -

Pullbacks of hyperplane sections for Lagrangian fibrations are primitive

Abstract

Keywords

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