Algebra & Number Theory

Deformations of smooth complete toric varieties: obstructions and the cup product

Nathan Ilten and Charles Turo

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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.

Article information

Source
Algebra Number Theory, Volume 14, Number 4 (2020), 907-926.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1593482422

Digital Object Identifier
doi:10.2140/ant.2020.14.907

Mathematical Reviews number (MathSciNet)
MR4114060

Zentralblatt MATH identifier
07224494

Subjects
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14B12: Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10] 14D15: Formal methods; deformations [See also 13D10, 14B07, 32Gxx]

Keywords
deformation theory toric varieties cup product

Citation

Ilten, Nathan; Turo, Charles. Deformations of smooth complete toric varieties: obstructions and the cup product. Algebra Number Theory 14 (2020), no. 4, 907--926. doi:10.2140/ant.2020.14.907. https://projecteuclid.org/euclid.ant/1593482422


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