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Mathematics, Differential Geometry, Mathematical Physics, Algebraic Geometry, Classical Analysis and ODEs
Abstract:
We extend the analytic theory of Frobenius manifolds to semisimple points
with coalescing eigenvalues of the operator of multiplication by the Euler
vector field. We clarify which freedoms, ambiguities and mutual constraints are
allowed in the definition of monodromy data, in view of their importance for
conjectural relationships between Frobenius manifolds and derived categories.
Detailed examples and applications are taken from singularity and quantum
cohomology theories. We explicitly compute the monodromy data at points of the
Maxwell Stratum of the A3-Frobenius manifold, as well as at the small quantum
cohomology of the Grassmannian G(2,4). In the latter case, we analyse in
details the action of the braid group on the monodromy data. This proves that
these data can be expressed in terms of characteristic classes of mutations of
Kapranov's exceptional 5-block collection, as conjectured by one of the
authors.
