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Trudy Mat. Inst. Steklova, 2007, Volume 258, Pages 58–69 (Mi tm476)  

This article is cited in 13 scientific papers (total in 13 papers)

On the Power Structure over the Grothendieck Ring of Varieties and Its Applications

S. M. Gusein-Zadea, I. Luengob, A. Melle-Hernándezb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Departamento de Álgebra, Universidad Complutense de Madrid

Abstract: We discuss the notion of a power structure over a ring and the geometric description of the power structure over the Grothendieck ring of complex quasi-projective varieties and show some examples of applications to generating series of classes of configuration spaces (for example, nested Hilbert schemes of J. Cheah) and wreath product orbifolds.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 258, 53–64

Bibliographic databases:

UDC: 512.56
Received in October 2006

Citation: S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “On the Power Structure over the Grothendieck Ring of Varieties and Its Applications”, Analysis and singularities. Part 1, Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 258, Nauka, MAIK Nauka/Inteperiodika, M., 2007, 58–69; Proc. Steklov Inst. Math., 258 (2007), 53–64

Citation in format AMSBIB
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\by S.~M.~Gusein-Zade, I.~Luengo, A.~Melle-Hern\'andez
\paper On the Power Structure over the Grothendieck Ring of Varieties and Its Applications
\inbook Analysis and singularities. Part~1
\bookinfo Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 258
\pages 58--69
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm476}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 258
\pages 53--64
\crossref{https://doi.org/10.1134/S0081543807030066}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35148878851}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Generating Series of Classes of Hilbert Schemes of Points on Orbifolds”, Proc. Steklov Inst. Math., 267 (2009), 125–130  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Tamanoi H., “Infinite product decomposition of orbifold mapping spaces”, Algebr. Geom. Topol., 9:1 (2009), 569–592  crossref  mathscinet  zmath  isi  scopus
    3. Gusein-Zade S.M., Luengo I., Melle-Hernandez A., “On the Pre-Lambda-Ring Structure on the Grothendieck Ring of Stacks and the Power Structures Over It”, Bull. London Math. Soc., 45:3 (2013), 520–528  crossref  mathscinet  zmath  isi  elib  scopus
    4. Gusein-Zade S.M., Luengo I., Melle-Hernandez A., “Higher-Order Orbifold Euler Characteristics For Compact Lie Group Actions”, Proc. R. Soc. Edinb. Sect. A-Math., 145:6 (2015), 1215–1222  crossref  mathscinet  zmath  isi  elib  scopus
    5. Gusein-Zade S.M., Luengo I., Melle-Hernandez A., “Higher Order Generalized Euler Characteristics and Generating Series”, J. Geom. Phys., 95 (2015), 137–143  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Equivariant versions of higher order orbifold Euler characteristics”, Mosc. Math. J., 16:4 (2016), 751–765  mathnet  crossref  mathscinet
    7. S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Russian Math. Surveys, 72:1 (2017), 1–32  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Farsi C., Seaton Ch., “Functional Equations For Orbifold Wreath Products”, J. Geom. Phys., 120 (2017), 37–51  crossref  mathscinet  zmath  isi  scopus
    9. Gusein-Zade S.M., Luengo I., Melle-Hernandez A., “Power Structure Over the Grothendieck Ring of Maps”, Rev. Mat. Complut., 31:3 (2018), 595–609  crossref  mathscinet  isi  scopus
    10. S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “The Universal Euler Characteristic of $V$-Manifolds”, Funct. Anal. Appl., 52:4 (2018), 297–307  mathnet  crossref  crossref  mathscinet  isi  elib
    11. Howe S., “Motivic Random Variables and Representation Stability II: Hypersurface Sections”, Adv. Math., 350 (2019), 1267–1313  crossref  isi
    12. Gusein-Zade S.M., Luengo I., Melle-Hernandez A., “Generalized Orbifold Euler Characteristics on the Grothendieck Ring of Varieties With Actions of Finite Groups”, Symmetry-Basel, 11:7 (2019), 902  crossref  mathscinet  isi
    13. Howe S., “Motivic Random Variables and Representation Stability i: Configuration Spaces”, Algebr. Geom. Topol., 20:6 (2020), 3013–3045  crossref  mathscinet  isi
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