Counting Points and Hilbert Series in String Theory

Abstract

The problem of counting points is revisited from the perspective of reflexive 4-dimensional polytopes. As an application, the Hilbert series of the 473,800,776 reflexive polytopes (equivalently, their Calabi-Yau hypersurfaces) are computed.

13 pages, 4 figures. Contribution to the Max Kreuzer memorial volume

References in corpus (1)

• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry

Cited by in corpus (3)

• Hilbert Series, Machine Learning, and Applications to Physics
• Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
• Dimensional interpolation and the Selberg integral