The Virasoro conjecture in Gromov-Witten theory asserts that the total ordinary descendant potential of a smooth projective complex variety satisfies a system of target-dependent
differential equations. Writing 
for the connected genus-
potential, the total potential is
 |
The constraints are
 |
The operators use the Poincaré pairing, the first Hodge degree 
on 
, and cup product with
,
with cohomological parity and a specified zero-mode scalar correction. The equations
are formal coefficientwise identities in genus, actual integral curve class, and
descendants.
