In algebraic geometry, the Virasoro conjecture states that a certain generating function encoding

Gromov–Witten invariant In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic man ...

s of a

smooth Smooth may refer to: Mathematics * Smooth function, a function that is infinitely differentiable; used in calculus and topology * Smooth manifold, a differentiable manifold for which all the transition maps are smooth functions * Smooth algebrai ...

projective variety is fixed by an action of half of the

Virasoro algebra In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string the ...

. The Virasoro conjecture is named after

theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experime ...

Miguel Ángel Virasoro. proposed the Virasoro conjecture as a generalization of

Witten's conjecture In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper , and generalized in . Witten's original conjecture was proved by Maxi ...

. gave a survey of the Virasoro conjecture.

References

* * Algebraic geometry Conjectures Unsolved problems in geometry {{algebraic-geometry-stub