Locally nilpotent derivations of graded integral domains and cylindricity

Autor:	Chitayat, Michael, Daigle, Daniel
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra Primary: 13N15 14R20. Secondary: 14C20 14R05 14R25
Druh dokumentu:	Working Paper
Popis:	Let B be a commutative $\mathbb{Z}$-graded domain of characteristic zero. An element f of B is said to be cylindrical if it is nonzero, homogeneous of nonzero degree, and such that $B_{(f)}$ is a polynomial ring in one variable over a subring. We study the relation between the existence of a cylindrical element of B and the existence of a nonzero locally nilpotent derivation of B. Also, given d > 0, we give sufficient conditions that guarantee that every derivation of $B^{(d)} = \oplus_i B_{di}$ can be extended to a derivation of B. We generalize some results of Kishimoto, Prokhorov and Zaidenberg that relate the cylindricity of a polarized projective variety (Y,H) to the existence of a nontrivial G_a-action on the affine cone over (Y,H). Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.01729 Zobrazit plný text záznamu View this record from Arxiv