Year: 2026
Type: article
Abstract: We study locally trivial deformations of toric varieties from a combinatorial point of view. For any fan Σ \Sigma , we construct a deformation functor Def Σ \operatorname {Def}_{\Sigma } by considering Čech zero-cochains on certain simplicial complexes. We show that under appropriate hypotheses, Def Σ \operatorname {Def}_{\Sigma } is isomorphic to Def X Σ ′ \operatorname {Def}’_{X_{\Sigma }} , the functor of locally trivial deformations for the toric variety X Σ X_{\Sigma } associated to Σ \Sigma . In particular, for any complete toric variety X X that is smooth in codimension 2 2 and Q \mathbb {Q} -factorial in codimension 3 3 , there exists a fan Σ \Sigma such that Def Σ \operatorname {Def}_{\Sigma } is isomorphic to Def X \operatorname {Def}_{X} , the functor of deformations of
Source: Journal of Algebraic Geometry
DOI: 10.1090/jag/868
Authors: Nathan Ilten, Sharon Robins
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403782799