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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 1, Pages 42–49
DOI: https://doi.org/10.4213/faa4176 (Mi faa4176) 		 
Grothendieck ring of pairs of quasi-projective varieties

Sabir Gusein-Zadeabc, Ignacio Luengod, Alejandro Melle-Hernándeze

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Moscow Center for Fundamental and Applied Mathematics
c NRU Higher School of Economics, Moscow, Russia
d Departamento de Álgebra, Universidad Complutense de Madrid
e Institute of Interdisciplinary Mathematics, Department of Algebra, Geometry, and Topology, Complutense University of Madrid
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DOI: https://doi.org/10.4213/faa4176
Abstract: We define a Grothendieck ring of pairs of complex quasi-projective varieties (consisting of a variety and a subvariety). We describe $\lambda$-structures on this ring and a power structure over it. We show that the conjectual symmetric power of the projective line with several orbifold points described by A. Fonarev is consistent with the symmetric power of this line with the set of distinguished points as a pair of varieties.
Keywords: complex quasi-projective varieties, Grothendieck rings, lambda-structures, power structures.
Funding agency Grant number
Russian Science Foundation 21-11-00080
Ministerio de Economía y Competitividad de España MTM PID2020-114750GB-C32
The work of the first author (§§\ref{sec:lambda} and \ref{sec:Example}) was supported by the grant no. 21-11-00080, of the Russian Science Foundation, https://rscf.ru/en/project/21-11-00080/. The work of the last two authors was supported by a competitive Spanish national grant MTM PID2020-114750GB-C32.
Received: 17.11.2023
Revised: 17.11.2023
Accepted: 20.11.2023
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 1, Pages 33–38
DOI: https://doi.org/10.1134/S0016266324010040
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Sabir Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernández, “Grothendieck ring of pairs of quasi-projective varieties”, Funktsional. Anal. i Prilozhen., 58:1 (2024), 42–49; Funct. Anal. Appl., 58:1 (2024), 33–38
Citation in format AMSBIB
\Bibitem{GusLueMel24}
\by Sabir Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hern\'andez
\paper Grothendieck ring of pairs of quasi-projective varieties
\jour Funktsional. Anal. i Prilozhen.
\yr 2024
\vol 58
\issue 1
\pages 42--49
\mathnet{http://mi.mathnet.ru/faa4176}
\crossref{https://doi.org/10.4213/faa4176}
\transl
\jour Funct. Anal. Appl.
\yr 2024
\vol 58
\issue 1
\pages 33--38
\crossref{https://doi.org/10.1134/S0016266324010040}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85193523664}
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