Grothendieck ring of varieties with finite groups actions

We define a Grothendieck ring of varieties with finite groups actions and show that the orbifold Euler characteristic and the Euler characteristics of higher orders can be defined as homomorphisms from this ring to the ring of integers. We describe two natural [landa]-structures on the ring and the...

Descripción completa

Detalles Bibliográficos
Autores: Gusein Zade, Sabir Medgidovich, Luengo, I., Melle Hernández, Alejandro
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/12884
Acceso en línea:https://hdl.handle.net/20.500.14352/12884
Access Level:acceso abierto
Palabra clave:512
Finite group actions
Complex quasi-projective varieties
Grothendieck rings
Lambda-structure
Power structure
Álgebra
1201 Álgebra
Descripción
Sumario:We define a Grothendieck ring of varieties with finite groups actions and show that the orbifold Euler characteristic and the Euler characteristics of higher orders can be defined as homomorphisms from this ring to the ring of integers. We describe two natural [landa]-structures on the ring and the corresponding power structures over it and show that one of these power structures is effective. We define a Grothendieck ring of varieties with equivariant vector bundles and show that the generalized ("motivic") Euler characteristics of higher orders can be defined as homomorphisms from this ring to the Grothendieck ring of varieties extended by powers of the class of the complex affine line. We give an analogue of the Macdonald type formula for the generating series of the generalized higher order Euler characteristics of wreath products.