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arXiv · 1808.04590

Cracked Polytopes and Fano Toric Complete Intersections

Thomas Prince
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Abstract

We introduce the notion of cracked polytope, and - making use of joint work with Coates and Kasprzyk - construct the associated toric variety $X$ as a subvariety of a non-singular toric variety $Y$ under certain conditions. Restricting to the case in which this subvariety is a complete intersection, we present a sufficient condition for a smoothing of $X$ to exist inside $Y$. We exhibit a relative anti-canonical divisor for this smoothing of $X$, and show that the general member is simple normal crossings.

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Thomas Prince. 2018-08-14. Cracked Polytopes and Fano Toric Complete Intersections. https://doi.org/10.1007/s00229-019-01149-2

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