The Hartogs extension phenomenon in toric varieties
Sergey Feklistov, Alexey Shchuplev
TL;DR
This paper investigates the Hartogs extension phenomenon in non-compact toric varieties, linking it to the fan structure and cohomology, and confirms a conjecture relating geometric conditions to extension properties.
Contribution
It establishes a criterion based on fan geometry for the Hartogs extension phenomenon in toric varieties, confirming a previous conjecture.
Findings
Extension occurs if a connected component of the fan complement is concave
The phenomenon is characterized by the first cohomology group with compact support
Confirms conjecture by M. Marciniak
Abstract
We study the Hartogs extension phenomenon in non-compact toric varieties and its relation to the first cohomology group with compact support. We show that a toric variety admits this phenomenon if at least one connected component of the fan complement is concave, proving by this an earlier conjecture M. Marciniak.
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