On a Morelli type expression of cohomology classes of toric varieties
Akio Hattori

TL;DR
This paper presents a canonical expression for homology classes of complete $Q$-factorial toric varieties as linear combinations of orbit closure classes, generalizing Morelli's Todd class formula using rational functions on Grassmannians.
Contribution
It introduces a new canonical method to express homology classes of toric varieties in terms of orbit closures, extending Morelli's formula with rational function coefficients.
Findings
Provides a canonical linear combination representation of homology classes.
Generalizes Morelli's formula for Todd classes.
Uses rational functions on Grassmannians for coefficients.
Abstract
Let be a complete -factorial toric variety of dimension and the fan in a lattice associated to . For each cone of there corresponds an orbit closure of the action of complex torus on . The homology classes form a set of specified generators of . It is shown that, given , there is a canonical way to express as a linear combination of the with coefficients in the field of rational functions of degree on the Grassmann manifold of -planes in . This generalizes Morelli's formula for the -th component of the Todd homology class of the variety .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models
