Families of pointed toric varieties and degenerations

Sandra Di Rocco; Luca Schaffler

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arXiv · 2110.04842

Families of pointed toric varieties and degenerations

Sandra Di Rocco·Luca Schaffler

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Abstract

The Losev-Manin moduli space parametrizes pointed chains of projective lines. In this paper we study a possible generalization to families of pointed degenerate toric varieties. Geometric properties of these families, such as flatness and reducedness of the fibers, are explored via a combinatorial characterization. We show that such families are described by a specific type of polytope fibration which generalizes the twisted Cayley sums, originally introduced to characterize elementary extremal contractions of fiber type associated to projective $\mathbb{Q}$-factorial toric varieties with positive dual defect. The case of a one-dimensional simplex can be viewed as an alternative construction of the permutohedra.

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Sandra Di Rocco, Luca Schaffler. 2021-10-10. Families of pointed toric varieties and degenerations. https://arxiv.org/abs/2110.04842

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