Lambda g conjecture

In algebraic geometry, the formula_1-conjecture gives a particularly simple formula for certain integrals on the Deligne–Mumford compactification formula_2 of the moduli space of curves with marked points. It was first found as a consequence of the Virasoro conjecture by . Later, it was proven by using virtual localization in Gromov–Witten theory. It is named after the factor of formula_1, the "g"th Chern class of the Hodge bundle, appearing in its integrand. The other factor is a monomial in the formula_4, the first Chern classes of the "n" cotangent line bundles, as in Witten's conjecture.
Let formula_5 be positive integers such that:
Then the formula_1-formula can be stated as follows:
The formula_1-formula in combination with
where the "B"2"g" are Bernoulli numbers, gives a way to calculate all integrals on formula_2 involving products in formula_12-classes and a factor of formula_1.