Contraction images of toric varieties
Hiromu Tanaka

TL;DR
This paper proves that proper morphisms from toric varieties to normal varieties preserve toric structure, ensuring the target is also toric and the morphism is toric under compatible structures.
Contribution
It establishes that any proper morphism from a toric variety to a normal variety with trivial pushforward of structure sheaf is necessarily toric, confirming the stability of toric structures under such morphisms.
Findings
Y is toric if X is toric and f is proper with f_*O_X = O_Y
f is a toric morphism for some toric structures on X and Y
Y inherits toric structure from X under the given conditions
Abstract
Let be a proper morphism of normal varieties with . If is toric, then is toric and is a toric morphism for some toric structures on and .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models
