Geodesic
Grothendieck ring of pairs of quasi-projective varieties
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 42-49 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, power structures.
Mots-clés : lambda-structures 
@article{FAA_2024_58_1_a3,
     author = {Sabir Gusein-Zade and Ignacio Luengo and Alejandro Melle-Hern\'andez},
     title = {Grothendieck ring of pairs of quasi-projective varieties},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {42--49},
     year = {2024},
     volume = {58},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a3/}
}
TY  - JOUR
AU  - Sabir Gusein-Zade
AU  - Ignacio Luengo
AU  - Alejandro Melle-Hernández
TI  - Grothendieck ring of pairs of quasi-projective varieties
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2024
SP  - 42
EP  - 49
VL  - 58
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a3/
LA  - ru
ID  - FAA_2024_58_1_a3
ER  - 
%0 Journal Article
%A Sabir Gusein-Zade
%A Ignacio Luengo
%A Alejandro Melle-Hernández
%T Grothendieck ring of pairs of quasi-projective varieties
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2024
%P 42-49
%V 58
%N 1
%U http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a3/
%G ru
%F FAA_2024_58_1_a3
Sabir Gusein-Zade; Ignacio Luengo; Alejandro Melle-Hernández. Grothendieck ring of pairs of quasi-projective varieties. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 42-49. http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a3/

[1] A. V. Fonarev, “Proizvodnaya kategoriya prostranstva modulei parabolicheskikh rassloenii na $\mathbb{P}^1$”, UMN, 78:3(471) (2023), 177–178 ; arXiv: 2305.18058 | DOI | MR

[2] S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “A power structure over the Grothendieck ring of varieties”, Math. Res. Lett., 11:1 (2004), 49–57 | DOI | MR | Zbl

[3] S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points”, Michigan Math. J., 54:2 (2006), 353–359 | DOI | MR | Zbl

[4] S. M. Gusein-Zade, I. Luengo, A. Mele-Ernandez, “O stepennoi strukture nad koltsom Grotendika mnogoobrazii i ee prilozheniyakh”, Trudy MIAN, 258 (2007), 58–69 | Zbl

[5] S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Grothendieck ring of varieties with actions of finite groups”, Proc. Edinb. Math. Soc. (2), 62:4 (2019), 925–948 | DOI | MR | Zbl

[6] D. Knutson, $\lambda$-rings and the representation theory of the symmetric group, Lecture Notes in Mathematics, no. 308, Springer-Verlag, Berlin–New York, 1973 | DOI | MR | Zbl

[7] A. Morrison, J. Shen, “Hodge numbers of generalized Kummer schemes via relative power structures”, Mosc. Math. J., 21:4 (2021), 807–830 | DOI | MR | Zbl