A classification algorithm for reflexive simplices

2025/10/10 by Marco Ghirlanda, Ghirlanda, Marco · 1 citation
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2510.09131

Abstract

We present a general classification algorithm for reflexive simplices, which allows us to determine all reflexive simplices in dimensions five and six. In terms of algebraic geometry this means that we classify the Gorenstein fake weighted projective spaces in dimensions five and six. As a byproduct of our methods, we obtain explicit formulae for the Picard group and the Gorenstein index of any fake weighted projective space.

Citations

• Sharp volume and multiplicity bounds for Fano simplices
• Automorphisms of finite Abelian groups
• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
• Complete classification of reflexive polyhedra in four dimensions
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

Cited by

• On Gorenstein Fano toric complete intersections

Related

• Classifying terminal weighted projective space
• The Integer Decomposition Property and Weighted Projective Space Simplices
• Sharp degree bounds for fake weighted projective spaces
• Q-factorial Gorenstein toric Fano varieties with large Picard number
• Gorenstein toric Fano varieties