Abstract
We define the ℤ2 Hodge spacesH pq (Σ) of a rational fan Σ. If Σ is the normal fan of a reflexive polytope Δ then we use polyhedral duality to compute the Σ2 Hodge Spaces of Σ. In particular, if the cones of dimension at most e in the face fan Σ* of Δ are smooth then we computeH pq (Σ) forp <e − 1. If Σ* is a smooth fan then we completely determine the spacesH pq (Σ) and we showX Σ is maximal, meaning that the sum of the ℤ2 Betti numbers ofX Σ(ℝ) is equal to the sum of the ℤ2 Betti numbers ofX Σ(ℂ).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
