The Virasoro conjecture, in algebraic geometry, 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. It is named after theoretical physicist Miguel Angel Virasoro and was proposed as a generalization of Witten's conjecture; the genus 0 case was proved for all smooth projective varieties by Xiaobo Liu and Gang Tian in 1998. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementA generating function encoding the Gromov-Witten invariants of a smooth projective variety is fixed by an action of half of the Virasoro algebra. 1 Proposed Year Progress Toward ResolutionThe genus zero case of the conjecture was proved for all smooth projective varieties by Xiaobo Liu and Gang Tian in 1998; the conjecture beyond genus zero remains open. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
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Source Virasoro Conjecture (Wikipedia)
Sources
1. Virasoro Conjecture (Wikipedia)
Formal statement section
A certain generating function encoding Gromov-Witten invariants of a smooth projective variety is fixed by an action of half of the Virasoro algebra.
History section, proof note
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).
- Lead section
View the Source2. Virasoro Conjecture (Wikipedia)
Wikimedia FoundationLead section
was first given by Xiaobo Liu and Gang Tian (1998)
Lead section, proposal sentence
Tohru Eguchi, Kentaro Hori, and Chuan-Sheng Xiong (1997) proposed the Virasoro conjecture
- In Branch: Algebraic Geometry, Lead sentence
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