Geodesic
Symmetric powers of Severi–Brauer varieties
Kollár, János1
1 Princeton University, Princeton NJ 08544-1000, USA
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 4, pp. 849-862.

Voir la notice de l'article provenant de la source Numdam

We classify products of symmetric powers of a Severi–Brauer variety, up to stable birational equivalence. The description also includes Grassmannians, flag varieties and moduli spaces of genus 0 stable maps.

Nous classons les produits de puissances symétriques d’une variété de Severi–Brauer, à équivalence birationnelle stable près. Notre classification concerne aussi les grassmanniennes, les variétés de drapeaux et les espaces de modules d’applications stables de genre 0.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1584

Kollár, János 1

1 Princeton University, Princeton NJ 08544-1000, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{AFST_2018_6_27_4_849_0,
     author = {Koll\'ar, J\'anos},
     title = {Symmetric powers of {Severi{\textendash}Brauer} varieties},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {849--862},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 27},
     number = {4},
     year = {2018},
     doi = {10.5802/afst.1584},
     mrnumber = {3884611},
     zbl = {1423.14092},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/afst.1584/}
}
TY  - JOUR
AU  - Kollár, János
TI  - Symmetric powers of Severi–Brauer varieties
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2018
SP  - 849
EP  - 862
VL  - 27
IS  - 4
PB  - Université Paul Sabatier, Toulouse
UR  - http://geodesic.mathdoc.fr/articles/10.5802/afst.1584/
DO  - 10.5802/afst.1584
LA  - en
ID  - AFST_2018_6_27_4_849_0
ER  - 
%0 Journal Article
%A Kollár, János
%T Symmetric powers of Severi–Brauer varieties
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2018
%P 849-862
%V 27
%N 4
%I Université Paul Sabatier, Toulouse
%U http://geodesic.mathdoc.fr/articles/10.5802/afst.1584/
%R 10.5802/afst.1584
%G en
%F AFST_2018_6_27_4_849_0
Kollár, János. Symmetric powers of Severi–Brauer varieties. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 4, pp. 849-862. doi : 10.5802/afst.1584. http://geodesic.mathdoc.fr/articles/10.5802/afst.1584/

[1] Alexeev, Valery Moduli spaces M g,n (W) for surfaces, Higher dimensional complex varieties (Trento, 1994), Walter de Gruyter (1996), pp. 1-22 | Zbl

[2] Araujo, Carolina; Kollár, János Rational curves on varieties, Higher dimensional varieties and rational points (Budapest, 2001) (Bolyai Society Mathematical Studies), Volume 12, Springer, 2003, pp. 13-68 | DOI | MR | Zbl

[3] Brion, Michel Lectures on the geometry of flag varieties, Topics in cohomological studies of algebraic varieties (Trends in Mathematics), Birkhäuser, 2005, pp. 33-85 | DOI

[4] Dolgachev, Igor V. Rationality of fields of invariants, Algebraic geometry (Bowdoin, 1985) (Proceedings of Symposia in Pure Mathematics), Volume 46, American Mathematical Society (1985), pp. 3-16 | Zbl

[5] Formanek, Edward The ring of generic matrices, J. Algebra, Volume 258 (2002) no. 1, pp. 310-320 | DOI | MR | Zbl

[6] Fulton, William; Pandharipande, Rahul Notes on stable maps and quantum cohomology, Algebraic geometry (Santa Cruz 1995) (Proceedings of Symposia in Pure Mathematics), Volume 62, American Mathematical Society (1995), pp. 45-96 | Zbl

[7] Gille, Philippe; Szamuely, Tamàs Central simple algebras and Galois cohomology, Cambridge Studies in Advanced Mathematics, 101, Cambridge University Press, 2006, xi+343 pages | MR | Zbl

[8] Hirschowitz, André La rationalité des schémas de Hilbert de courbes gauches rationnelles suivant Katsylo, Algebraic curves and projective geometry (Trento, 1988) (Lecture Notes in Mathematics), Volume 1389, Springer (1988), pp. 87-90 | DOI | Zbl

[9] Hodge, William Vallance Douglas; Pedoe, Daniel Methods of Algebraic Geometry. Vols. I–III., Cambridge University Press, 1947, 1952, 1954

[10] Hogadi, Amit Products of Brauer-Severi surfaces, Proc. Am. Math. Soc., Volume 137 (2009) no. 1, pp. 45-50 | DOI | MR | Zbl

[11] Katsylo, Pavel I. Rationality of fields of invariants of reducible representations of the group SL 2 , Vestn. Mosk. Univ., Volume 1984 (1984) no. 5, pp. 77-79 | MR | Zbl

[12] Kim, Bumsig; Pandharipande, Rahul The connectedness of the moduli space of maps to homogeneous spaces, Symplectic geometry and mirror symmetry (Seoul, 2000), World Scientific, 2000, pp. 187-201 | Zbl

[13] Kollár, János Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 32, Springer, 1996, viii+320 pages | MR | Zbl

[14] Kollár, János Conics in the Grothendieck ring, Adv. Math., Volume 198 (2005) no. 1, pp. 27-35 | DOI | MR | Zbl

[15] Kollár, János Severi–Brauer varieties; a geometric treatment (2016) (https://arxiv.org/abs/1606.04368)

[16] Kollár, János; Smith, Karen E.; Corti, Alessio Rational and nearly rational varieties, Cambridge Studies in Advanced Mathematics, 92, Cambridge University Press, 2004, vi+235 pages | MR | Zbl

[17] Krashen, Daniel Zero cycles on homogeneous varieties, Adv. Math., Volume 223 (2010) no. 6, pp. 2022-2048 | DOI | MR | Zbl

[18] Krashen, Daniel; Saltman, David J. Severi–Brauer varieties and symmetric powers, Algebraic transformation groups and algebraic varieties (Encyclopaedia of Mathematical Sciences), Volume 132, Springer, 2090, pp. 59-70 | DOI | Zbl

[19] Kresch, Andrew Flag varieties and Schubert calculus, Algebraic groups (Göttingen, 2007) (Mathematisches Institut. Seminare), Universitätsverlag Göttingen, 2007, pp. 73-86 | Zbl

[20] Mattuck, Arthur The field of multisymmetric functions, Proc. Am. Math. Soc., Volume 19 (1968), pp. 764-765 | MR | Zbl

[21] Weil, André Foundations of algebraic geometry, American Mathematical Society Colloquium Publications, XXIX, American Mathematical Society, 1962, xx+363 pages | Zbl

Cité par Sources :