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

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