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2020 Deformations of smooth complete toric varieties: obstructions and the cup product
Nathan Ilten, Charles Turo
Algebra Number Theory 14(4): 907-926 (2020). DOI: 10.2140/ant.2020.14.907

Abstract

Let X be a complete -factorial toric variety. We explicitly describe the space H2(X,𝒯X) and the cup product map H1(X,𝒯X)×H1(X,𝒯X)H2(X,𝒯X) in combinatorial terms. Using this, we give an example of a smooth projective toric threefold for which the cup product map does not vanish, showing that in general, smooth complete toric varieties may have obstructed deformations.

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Nathan Ilten. Charles Turo. "Deformations of smooth complete toric varieties: obstructions and the cup product." Algebra Number Theory 14 (4) 907 - 926, 2020. https://doi.org/10.2140/ant.2020.14.907

Information

Received: 2 January 2019; Revised: 25 November 2019; Accepted: 6 February 2020; Published: 2020
First available in Project Euclid: 30 June 2020

zbMATH: 07224494
MathSciNet: MR4114060
Digital Object Identifier: 10.2140/ant.2020.14.907

Subjects:
Primary: 14M25
Secondary: 14B12 , 14D15

Keywords: cup product , deformation theory , toric varieties

Rights: Copyright © 2020 Mathematical Sciences Publishers

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