Conic decomposition of a toric variety and its application to cohomology
Abstract
We introduce the notion of a \emph{conic sequence} of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one with certain regulations. We apply this to a toric variety to obtain an iterated cofibration structure on it. This allows us to prove several vanishing results in the rational cohomology of a toric variety and to calculate Poincaré polynomials for a large class of singular toric varieties.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.04429
- arXiv:
- arXiv:2106.04429
- Bibcode:
- 2021arXiv210604429P
- Keywords:
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- Mathematics - Algebraic Topology;
- Mathematics - Algebraic Geometry;
- Mathematics - Combinatorics;
- 14M25;
- 55N10;
- 52B05;
- 52B11
- E-Print:
- 14 pages, 6 figures