QuiversToricVarieties: a package to construct quivers of sections on complete toric varieties
Nathan Prabhu-Naik
TL;DR
QuiversToricVarieties is a Macaulay2 package that constructs quivers of sections for line bundles on complete toric varieties and verifies strong exceptionality, with a database for smooth Fano cases up to dimension 4.
Contribution
It introduces a computational tool for constructing and analyzing quivers of line bundles on toric varieties, including a database for specific Fano cases.
Findings
Provides a practical method for quiver construction on toric varieties.
Includes a database of strong exceptional collections for smooth Fano toric varieties.
Enables verification of strong exceptionality of collections.
Abstract
Given a collection of line bundles on a complete toric variety, the Macaulay2 package QuiversToricVarieties contains functions to construct its quiver of sections and check whether the collection is strong exceptional. It contains a database of full strong exceptional collections of line bundles for smooth Fano toric varieties of dimension less than or equal to 4.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications