The Structure of Algebraic Families of Birational Transformations

Autor:	Regeta, Andriy, Urech, Christian, van Santen, Immanuel
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry 14E07 14L30
Druh dokumentu:	Working Paper
Popis:	We give a description of the algebraic families of birational transformations of an algebraic variety X. As an application, we show that the morphisms to Bir(X) given by algebraic families satisfy a Chevalley type result and a certain fibre-dimension formula. Moreover, we show that the algebraic subgroups of Bir(X) are exactly the closed finite-dimensional subgroups with finitely many components. We also study algebraic families of birational transformations preserving a fibration. This builds on previous work of Blanc-Furter, Hanamura, and Ramanujam. Comment: 28 pages, comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.06475 Zobrazit plný text záznamu View this record from Arxiv