Torus invariant divisors

By Lars Petersen, Hendrik Süß. 2008

75 citations recorded by the source corpus.

Using the language of Altmann, Hausen and Süß, we describe invariant divisors on normal varieties X which admit an effective codimension one torus action. In this picture, X is given by a divisorial fan on a smooth projective curve Y. Cartier divisors on X can be described by piecewise affine functions h on the divisorial fan S whereas Weil divisors correspond to certain zero and one-dimensional faces of it. Furthermore, we provide descriptions of the divisor class group and the canonical divisor. Global sections of line bundles O(Dh) will be determined by a subset of a weight polytope associated to h, and global sections of specific line bundles on the underlying curve Y.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ed18a10c9d2531a1ebe059733e21b1fcef25becc

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In Geometry and Topology

In Mathematical Physics

Hendrik Suss

Citations in the corpus

NORMAL SINGULARITIES WITH TORUS ACTIONS (2010, unknown): “Invariant T -divisors were studied in [PS08].”
K-stability for Fano manifolds with torus action of complexity $1$ (2015, background): “⊥ instead of Ne. We denote this p-divisor by D. Note that TV(D′) diﬀers from TV(De) by one exactly one (C∗×T×C∗)-invariant prime divisor H, corresponding to the special ﬁber X0. In the terminology of [PS11] there are two possibilities: His either horizontal or vertical. Suppose ﬁrst that His horizon”