Vol. 14, No. 4, 2020

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

Nathan Ilten and Charles Turo

Vol. 14 (2020), No. 4, 907–926
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.

Keywords
deformation theory, toric varieties, cup product
Mathematical Subject Classification 2010
Primary: 14M25
Secondary: 14B12, 14D15
Milestones
Received: 2 January 2019
Revised: 25 November 2019
Accepted: 6 February 2020
Published: 21 June 2020
Authors
Nathan Ilten
Simon Fraser University
Burnaby BC
Canada
Charles Turo
Simon Fraser University
Burnaby BC
Canada