Virasoro conjecture
In algebraic geometry, the Virasoro conjecture states that a certain generating function encoding Gromov–Witten invariants of a smooth projective variety is fixed by an action of half of the Virasoro algebra. The Virasoro conjecture is named after theoretical physicist Miguel Ángel Virasoro. Tohru Eguchi, Kentaro Hori, and Chuan-Sheng Xiong (1997) proposed the Virasoro conjecture as a generalization of Witten's conjecture. Ezra Getzler (1999) gave a survey of the Virasoro conjecture.
The proof of the genus 0 Virasoro conjecture for all smooth projective varieties (or more generally, compact symplectic manifolds) was first given by Xiaobo Liu and Gang Tian (1998).[1]
References
- ↑ Liu, Xiaobo; Tian, Gang (1998-10-20), Virasoro Constraints For Quantum Cohomology, arXiv:math/9806028, Bibcode:1998math......6028L, arXiv:math/9806028
- Getzler, Ezra (1999), "The Virasoro conjecture for Gromov-Witten invariants", in Wiśniewski, Jarosław; Szurek, Michał; Pragacz, Piotr (eds.), Algebraic geometry: Hirzebruch 70 (Warsaw, 1998), Contemporary Mathematics, vol. 241, Providence, R.I.: American Mathematical Society, pp. 147–176, arXiv:math/9812026, Bibcode:1998math.....12026G, doi:10.1090/conm/241/03634, ISBN 978-0-8218-1149-8, MR 1718143
- Eguchi, Tohru; Hori, Kentaro; Xiong, Chuan-Sheng (1997), "Quantum cohomology and Virasoro algebra", Physics Letters B, 402 (1): 71–80, arXiv:hep-th/9703086, Bibcode:1997PhLB..402...71E, doi:10.1016/S0370-2693(97)00401-2, ISSN 0370-2693, MR 1454328
- Liu, Xiaobo; Tian, Gang (1998-10-20), Virasoro Constraints For Quantum Cohomology, arXiv:math/9806028, Bibcode:1998math......6028L, arXiv:math/9806028
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