tt* geometry, Frobenius manifolds, their connections, and the construction for singularities
By C. Hertling. 2002
159 citations recorded by the source corpus.
The base space of a semiuniversal unfolding of a hypersurface singularity carries a rich geometry. By work of K. Saito and M. Saito is can be equipped with the structure of a Frobenius manifold. By work of Cecotti and Vafa it can be equipped with tt* geometry if the singularity is quasihomogeneous. tt* geometry generalizes the notion of variation of Hodge structures. In the second part of this paper (chapters 6-8) Frobenius manifolds and tt* geometry are constructed for any hypersurface singularity, using essentially oscillating integrals; and the intimate relationship between polarized mixed Hodge structures and this tt* geometry is worked out. In the first part (chapters 2-5) tt* geometry and Frobenius manifolds and their relations are studied in general. To both of them flat connections with poles are associated, with distinctive common and different properties. A frame for a simultaneous construction is given.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4b1e63f80812fb168c8dfcc43713c7496ce9a225
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Citations in the corpus
- Quantum Cohomology and Periods (2011, background): “Generalizations of Hodge structure have been studied by many people and referred to in various ways: semi-infinite Hodge structure [2, 37], TERP structure [31] and noncommutative Hodge structure [40] etc.”
- Hodge theoretic aspects of mirror symmetry (2008, background): “ory in the work of Hertling [ Her03 , Her06] and Hertling-Sevenchek [HS07] under the”