Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: Geometrically pure G_a-actions
Speaker: Buddhadev Hajra, TIFR, Mumbai
Date: April 23, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In the recent article doi.org/10.1016/j.jalgebra.2024.02.041, Masayoshi Miyanishi defined when an action of the additive algebraic group scheme G_a on an affine variety Y is said to be geometrically pure. Such a G_a-action guarantees the existence of a geometric quotient of Y by that action whenever Y is assumed to be normal. Namely, there exists the quotient morphism q: Y \to X to a normal affine variety X such that the graph morphism \Phi: G_a \times Y \to Y \times_{X} Y is an isomorphism. The geometric pure-ness of the given G_a-action is the first criterion ever to ensure the existence of a geometric quotient Y/G_a. As a consequence, an algebraic characterization of the affine 3-space is obtained in the above article. In my lecture, I will present this content through certain interesting properties of pure subrings of commutative rings.
Title of Talk: Geometrically pure G_a-actions
Speaker: Buddhadev Hajra, TIFR, Mumbai
Date: April 23, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In the recent article doi.org/10.1016/j.jalgebra.2024.02.041, Masayoshi Miyanishi defined when an action of the additive algebraic group scheme G_a on an affine variety Y is said to be geometrically pure. Such a G_a-action guarantees the existence of a geometric quotient of Y by that action whenever Y is assumed to be normal. Namely, there exists the quotient morphism q: Y \to X to a normal affine variety X such that the graph morphism \Phi: G_a \times Y \to Y \times_{X} Y is an isomorphism. The geometric pure-ness of the given G_a-action is the first criterion ever to ensure the existence of a geometric quotient Y/G_a. As a consequence, an algebraic characterization of the affine 3-space is obtained in the above article. In my lecture, I will present this content through certain interesting properties of pure subrings of commutative rings.