Hodge Spaces for Real Toric Varieties
Valerie Hower

TL;DR
This paper introduces Z/2Z Hodge spaces for real toric varieties, providing methods to compute them using polyhedral duality, especially for smooth fans, and establishing conditions for maximality of the associated real toric variety.
Contribution
It defines Z/2Z Hodge spaces for fans and develops computational techniques using polyhedral duality, including complete determination for smooth fans and criteria for maximality.
Findings
Computed Hodge spaces for reflexive polytope fans
Established conditions for maximality of real toric varieties
Demonstrated complete determination of H_{pq} for smooth fans
Abstract
We define the Z/2Z Hodge spaces H_{pq}(\Sigma) of a fan \Sigma. If \Sigma is the normal fan of a reflexive polytope \Delta then we use polyhedral duality to compute the Z/2Z Hodge Spaces of \Sigma. In particular, if the cones of dimension at most e in the face fan \Sigma^* of \Delta are smooth then we compute H_{pq}(\Sigma) for p<e-1. If \Sigma^* is a smooth fan then we completely determine the spaces H_{pq}(\Sigma) and we show the toric variety X associated to \Sigma is maximal, meaning that the sum of the Z/2Z Betti numbers of X(R) is equal to the sum of the Z/2Z Betti numbers of X(C).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry
