Geodesic
Vertex algebras and the formal loop space
Publications Mathématiques de l'IHÉS, Tome 100 (2004), pp. 209-269

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

We construct a certain algebro-geometric version ℒ(X) of the free loop space for a complex algebraic variety X. This is an ind-scheme containing the scheme ℒ 0 (X) of formal arcs in X as studied by Kontsevich and Denef-Loeser. We describe the chiral de Rham complex of Malikov, Schechtman and Vaintrob in terms of the space of formal distributions on ℒ(X) supported in ℒ 0 (X). We also show that ℒ(X) possesses a factorization structure: a certain non-linear version of a vertex algebra structure. This explains the heuristic principle that “all” linear constructions applied to the free loop space produce vertex algebras.

@article{PMIHES_2004__100__209_0,
     author = {Kapranov, Mikhail and Vasserot, Eric},
     title = {Vertex algebras and the formal loop space},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {209--269},
     publisher = {Springer},
     volume = {100},
     year = {2004},
     doi = {10.1007/s10240-004-0023-9},
     mrnumber = {2102701},
     zbl = {1106.17038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-004-0023-9/}
}
TY  - JOUR
AU  - Kapranov, Mikhail
AU  - Vasserot, Eric
TI  - Vertex algebras and the formal loop space
JO  - Publications Mathématiques de l'IHÉS
PY  - 2004
SP  - 209
EP  - 269
VL  - 100
PB  - Springer
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10240-004-0023-9/
DO  - 10.1007/s10240-004-0023-9
LA  - en
ID  - PMIHES_2004__100__209_0
ER  - 
%0 Journal Article
%A Kapranov, Mikhail
%A Vasserot, Eric
%T Vertex algebras and the formal loop space
%J Publications Mathématiques de l'IHÉS
%D 2004
%P 209-269
%V 100
%I Springer
%U http://geodesic.mathdoc.fr/articles/10.1007/s10240-004-0023-9/
%R 10.1007/s10240-004-0023-9
%G en
%F PMIHES_2004__100__209_0
Kapranov, Mikhail; Vasserot, Eric. Vertex algebras and the formal loop space. Publications Mathématiques de l'IHÉS, Tome 100 (2004), pp. 209-269. doi: 10.1007/s10240-004-0023-9

Cité par Sources :