42 research outputs found
Twisted Gromov-Witten r-spin potential and Givental's quantization
The universal curve p:C->\Mbar over the moduli space \Mbar of stable r-spin
maps to a target K\"ahler manifold X carries a universal spinor bundle L->C.
Therefore the moduli space \Mbar itself carries a natural K-theory class Rp_*L.
We introduce a twisted r-spin Gromov-Witten potential of X enriched with
Chern characters of Rp_*L. We show that the twisted potential can be
reconstructed from the ordinary r-spin Gromov-Witten potential of X via an
operator that assumes a particularly simple form in Givental's quantization
formalism.Comment: 25 pages, 3 figure
Changes of variables in ELSV-type formulas
In [5] I.P. Goulden, D.M. Jackson, and R. Vakil formulated a conjecture
relating certain Hurwitz numbers (enumerating ramified coverings of the sphere)
to the intersection theory on a conjectural Picard variety. We are going to use
their formula to study the intersection theory on this variety (if it is ever
to be constructed) by methods close to those of M. Kazarian and S. Lando in
[7]. In particular, we prove a Witten-Kontsevich-type theorem relating the
intersection theory and integrable hierarchies.
We also extend the results of [7] to include the Hodge integrals over the
moduli spaces, involving one lambda-class.Comment: 25 pages. Final versio