Birational types of algebraic orbifolds

Abstract

We introduce a variant of the birational symbols group of Kontsevich, Pestun and the second author, and use this to define birational invariants of algebraic orbifolds.

Cohomology of finite subgroups of the plane Cremona group

“…It is a stable G-birational invariant of X, as well as a stable birational invariant of the quotient stack [X/G], in the sense of [20,Sect. 4].…”

Equivariant Burnside groups and representation theory

“…Burnside groups of stacks. In [17] we defined Burn n , the Burnside group of orbifolds, receiving birational equivalence classes of algebraic orbifolds; we write [X ] ∈ Burn n for the class of the quotient stack X := [X/G]. In [16,Section 7] we defined a homomorphism…”

“…Let G be a finite group, and k a field of characteristic zero containing all roots of unity of order dividing |G|. In this paper, we continue the study of the equivariant Burnside group Burn n (G), introduced in [16], building on [15], [14], [17], and [13]. This group receives G-equivariant birational equivalence classes [X ý G] of smooth projective varieties X with generically free G-action.…”

A Refinement of the Motivic Volume, and Specialization of Birational Types

“…Thus the difference of these two classes lies in the kernel of the map K(Var dim Remark 2.3.4. A different manifestation of the isomorphism in Proposition 2.3.1 also appears in Proposition 2.2 of[KT21].…”