Algebraic algorithms for vector bundles over curves

Autor:	Montessinos, Mickaël
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry 14Q05 14H60 14H05 14-04 94B27
Druh dokumentu:	Working Paper
Popis:	We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and images of global homomorphisms, isomorphisms between vector bundles, cohomology groups, extensions, and splitting into a direct sum of indecomposables. Most algorithms are deterministic except for computing isomorphisms when the base field is infinite. Some algorithms are only polynomial time if we may compute Hermite forms of pseudo-matrices in polynomial time. All algorithms rely exclusively on algebraic operations in function fields. For applications, we give an algorithm enumerating isomorphism classes of vector bundles on an elliptic curve, and to construct algebraic geometry codes over vector bundles. We implement all our algorithms into a SageMath package. Comment: 39 pages. Comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.09449 Zobrazit plný text záznamu View this record from Arxiv