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 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.
Di Rocco, S., Schaffler, L. (2022). Families of pointed toric varieties and degenerations. MATHEMATISCHE ZEITSCHRIFT, 301(4), 4119-4139 [10.1007/s00209-022-03047-y].
Families of pointed toric varieties and degenerations
Schaffler, L
2022-01-01
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.