Grothendieck Ring of Varieties with Actions of Finite Groups

DOI10.1017/S001309151900004XzbMath1454.14023arXiv1706.00918MaRDI QIDQ5236937

Alejandro Melle-Hernández, Sabir M. Gusein-Zade, I. Luengo Velasco

Publication date: 16 October 2019

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.00918

zbMATH Keywords

Grothendieck ringsfinite group actionscomplex quasi-projective varietiespower structurelambda-structure

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Group actions on varieties or schemes (quotients) (14L30) Grothendieck groups (category-theoretic aspects) (18F30) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items

Mirror symmetry on levels of non-abelian Landau-Ginzburg orbifolds, Dual invertible polynomials with permutation symmetries and the orbifold Euler characteristic, The universal Euler characteristic of \(V\)-manifolds, Categorical measures for finite group actions

Cites Work

• Higher order generalized Euler characteristics and generating series
• Zeta functions, Grothendieck groups, and the Witt ring
• \(\lambda\)-rings and the representation theory of the symmetric group
• On equivariant Euler characteristics
• On the Euler number of an orbifold
• Orbifold Euler characteristics and the number of commuting \(m\)-tuples in the symmetric groups
• Topological orbifold models and quantum cohomology rings
• A power structure over the Grothendieck ring of varieties
• Rationality of motivic zeta functions for curves with finite abelian group actions
• The Betti numbers of \overline{ℳ}_{0,𝓃}(𝓇,𝒹)
• The McKay correspondence for finite subgroups of SL(3,\C)
• The universal Euler characteristic for varieties of characteristic zero
• On the pre-λ-ring structure on the Grothendieck ring of stacks and the power structures over it
• On equivariant versions of higher order orbifold Euler characteristics
• Generalized orbifold Euler characteristic of symmetric products and equivariant Morava \(K\)-theory
• Orbifold Hodge numbers of the wreath product orbifolds