Mathematics > Algebraic Geometry
[Submitted on 21 Dec 2018 (v1), last revised 7 Feb 2020 (this version, v2)]
Title:Deformations of Smooth Complete Toric Varieties: Obstructions and the Cup Product
View PDFAbstract:Let $X$ be a complete $\mathbb{Q}$-factorial toric variety. We explicitly describe the space $H^2(X,T_X)$ and the cup product map $H^1(X,T_X)\times H^1(X,T_X)\to H^2(X,T_X)$ 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.
Submission history
From: Nathan Ilten [view email][v1] Fri, 21 Dec 2018 16:51:32 UTC (19 KB)
[v2] Fri, 7 Feb 2020 16:10:50 UTC (18 KB)
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