Toric Ext and Tor in polymake and Singular: The Two-Dimensional Case and Beyond

DOI10.1007/978-3-319-70566-8_17zbMath1400.13001OpenAlexW2791562705MaRDI QIDQ4556584

Lars Kastner

Publication date: 16 November 2018

Published in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-70566-8_17

zbMATH Keywords

cyclic quotient singularitiescontinued fractionstoric geometry

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Homological dimension and commutative rings (13D05) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Software, source code, etc. for problems pertaining to algebraic geometry (14-04)

Uses Software

• cdd
• Normaliz
• polymake
• SINGULAR
• 4ti2
• Gfan
• homolog.lib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The \(\mathrm{GL}(2,{\mathbb{C}}\)) McKay correspondence
• Threefolds and deformations of surface singularities
• Zweidimensionale Quotientensingularitaeten: Gleichungen und Syzygien
• The versal deformation of an isolated toric Gorenstein singularity
• Reflexive modules on quotient surface singularities
• The dualizing sheaf on first-order deformations of toric surface singularities
• A Portable Parallel Implementation of the lrs Vertex Enumeration Code
• Introduction to Toric Varieties. (AM-131)
• Polytopes, Rings, and K-Theory
• Homological Algebra on a Complete Intersection, with an Application to Group Representations
• P-Resolutions of Cyclic Quotients from the Toric Viewpoint