Fibers over infinity of Landau-Ginzburg models

Ivan Cheltsov; VICTOR  PRZYJALKOWSKI

doi:10.4310/CNTP.2022.v16.n4.a1

Fibers over infinity of Landau-Ginzburg models

Ivan Cheltsov, VICTOR PRZYJALKOWSKI^*

^*Corresponding author for this work

School of Mathematics

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

Abstract

We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety X equals the dimension of the anticanonical system of X. We verify this conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.

Original language	English
Pages (from-to)	673-693
Number of pages	21
Journal	Communications in Number Theory and Physics
Volume	16
Issue number	4
DOIs	https://doi.org/10.4310/CNTP.2022.v16.n4.a1
Publication status	Published - 21 Oct 2022

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10.4310/CNTP.2022.v16.n4.a1

2005.01534Accepted author manuscript, 201 KB

https://arxiv.org/abs/2005.01534

The Calabi problem for smooth Fano threefolds
Cheltsov, I. (Principal Investigator)
EPSRC
1/05/22 → 30/04/24
Project: Research

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abstract = "We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety X equals the dimension of the anticanonical system of X. We verify this conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.",

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AB - We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety X equals the dimension of the anticanonical system of X. We verify this conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.

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Fibers over infinity of Landau-Ginzburg models

Abstract

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The Calabi problem for smooth Fano threefolds

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