Taylor Polynomials of Rational Functions

Autor:	Conca, Aldo, Naldi, Simone, Ottaviani, Giorgio, Sturmfels, Bernd
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Computer Science - Symbolic Computation Mathematics - Commutative Algebra
Druh dokumentu:	Working Paper
Popis:	A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on Hankel matrices. Inversion of the natural parametrization is known as Pad\'e approximation. We study the dimension and defining ideals of Taylor varieties. Taylor hypersurfaces are interesting for projective geometry, since their Hessians tend to vanish. In three and more variables, there exist defective Taylor varieties whose dimension is smaller than the number of parameters. We explain this with Fr\"oberg's Conjecture in commutative algebra. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.00712 Zobrazit plný text záznamu View this record from Arxiv