Next Article in Journal
A Hybrid Plithogenic Decision-Making Approach with Quality Function Deployment for Selecting Supply Chain Sustainability Metrics
Next Article in Special Issue
Definable Transformation to Normal Crossings over Henselian Fields with Separated Analytic Structure
Previous Article in Journal
Docking Linear Ligands to Glucose Oxidase
Previous Article in Special Issue
Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras
Open AccessArticle

Generalized Orbifold Euler Characteristics on the Grothendieck Ring of Varieties with Actions of Finite Groups

1
Faculty of Mechanics and Mathematics, Moscow State University, GSP-1, Moscow 119991, Russia
2
ICMAT (CSIC-UAM-UC3M-UCM), Department of Algebra, Geometry and Topology, Complutense University of Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
3
Instituto de Matemática Interdisciplinar (IMI), Department of Algebra, Geometry and Topology, Complutense University of Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 902; https://doi.org/10.3390/sym11070902
Received: 6 June 2019 / Revised: 5 July 2019 / Accepted: 9 July 2019 / Published: 11 July 2019
(This article belongs to the Special Issue Mirror Symmetry and Algebraic Geometry)
The notion of the orbifold Euler characteristic came from physics at the end of the 1980s. Coincidence (up to sign) of the orbifold Euler characteristics is a necessary condition for crepant resolutions of orbifolds to be mirror symmetric. There were defined higher order versions of the orbifold Euler characteristic and generalized (“motivic”) versions of them. In a previous paper, the authors defined a notion of the Grothendieck ring K 0 fGr ( Var C ) of varieties with actions of finite groups on which the orbifold Euler characteristic and its higher order versions are homomorphisms to the ring of integers. Here, we define the generalized orbifold Euler characteristic and higher order versions of it as ring homomorphisms from K 0 fGr ( Var C ) to the Grothendieck ring K 0 ( Var C ) of complex quasi-projective varieties and give some analogues of the classical Macdonald equations for the generating series of the Euler characteristics of the symmetric products of a space. View Full-Text
Keywords: actions of finite groups; complex quasi-projective varieties; Grothendieck rings; λ-structure; power structure; Macdonald-type equations actions of finite groups; complex quasi-projective varieties; Grothendieck rings; λ-structure; power structure; Macdonald-type equations
MDPI and ACS Style

Gusein-Zade, S.M.; Luengo, I.; Melle-Hernández, A. Generalized Orbifold Euler Characteristics on the Grothendieck Ring of Varieties with Actions of Finite Groups. Symmetry 2019, 11, 902. https://doi.org/10.3390/sym11070902

AMA Style

Gusein-Zade SM, Luengo I, Melle-Hernández A. Generalized Orbifold Euler Characteristics on the Grothendieck Ring of Varieties with Actions of Finite Groups. Symmetry. 2019; 11(7):902. https://doi.org/10.3390/sym11070902

Chicago/Turabian Style

Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A. 2019. "Generalized Orbifold Euler Characteristics on the Grothendieck Ring of Varieties with Actions of Finite Groups" Symmetry 11, no. 7: 902. https://doi.org/10.3390/sym11070902

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop