On Dubrovin's Frobenius structures on Hurwitz spaces

?

On Dubrovin's Frobenius structures on Hurwitz spaces

P. 221–236.

Hurwitz spaces are spaces of meromorphic functions on algebraic curves. B.Dubrovin introduced Frobenius structures on Hurwitz spaces, which serve as one of the most spectacular examples of such structures. On the other hand, Hurwitz spaces admit natural compactification by stable maps. The main goal of the present paper is to formulate a question concerning the behavior of Dubrovin's Frobenius structures on Hurwitz spaces on the boundary of the compactification. Sample computations justifying the question are given.

Language: English

Full text

In book

Advanced Studies in Pure Mathematics (Primitive Forms and Related Subjects - Kavli IPMU 2014)

Vol. 83: Primitive Forms and Related Subjects - Kavli IPMU 2014. , Tokyo: Mathematical Society of Japan, 2019.

A remark on deformations of Hurwitz Frobenius manifolds

Buryak A., Shadrin S., Letters in Mathematical Physics 2010 Vol. 93 No. 3 P. 243–252

In this note we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux-Egoroff system. As an application, we explain how Shramchenko's deformations of Frobenius manifold structures on Hurwitz spaces fit into the general formalism of Givental-van de Leur twisted loop group action on ...

Added: October 5, 2020

Universal Cohomological Expressions for Singularities in Families of Genus 0 Stable Maps

Kazaryan M., Zvonkine D., Lando S., International Mathematics Research Notices 2018 No. 22 P. 6817–6843

We consider families of curve-to-curve maps that have no singularities except those of genus 0 stable maps and that satisfy a versality condition at each singularity. We provide a universal expression for the cohomology class Poincaré dual to the locus of any given singularity. Our expressions hold for any family of curve-to-curve maps satisfying the ...

Added: July 10, 2017

Degrees of cohomological classes of multisinguliarities in Hurwitz spaces of rational functions

Bychkov B., / Series "Working papers by Cornell University". 2016.

The main goal of the present paper are new formulae for degrees of strata in Hurwitz spaces of rational functions having two degenerate critical values with preimages of prescribed multiplicities. We consider the case where the multiplicities of the preimages of one critical value are arbitrary, while the second critical value has degeneracy of codimension ...

Added: November 8, 2016