Hodge theoretic aspects of mirror symmetry

By L. Katzarkov, M. Kontsevich, T. Pantev. 2008

133 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c01b94df675f00f00748248e3302c181f4114493

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Citations in the corpus

Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures (2014, methodology): “tures for projective spaces and for Grassmannians. The Gamma Conjectures for Pn were implicit but essentially shown in the work of Dubrovin [17]; they also follow from mirror symmetry computations in [44,45,49]. In x5, we give an elementary proof of the following theorem. Theorem 1.3.1 (Theorem5.0.1”
Homological mirror symmetry for the genus two curve (2008, background): “ll form, but in many cases it should follow from the results presented there together with additional steps which are fundamentally well-understood. 1 2 PAUL SEIDEL Figure 1. More recently, Katzarkov [32, 37] has proposed a further extension of HMS encompassing some varieties of general type. As bef”
Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry (2013, background): “) on C−{xi}1≤i≤nendowed with the so-called Stokes structure. The local system consists of analytic germs of ﬂat sections of (E,∇). We are going to recall the notion of Stokes structure on C following [KaKoPa]. It describes the local picture on a general curve C. For any marked point xi and a generic”
An integral structure in quantum cohomology and mirror symmetry for toric orbifolds (2009, methodology): “from the bΓ-integral structure. After the 4 HIROSHI IRITANI preprint version [49] of this paper was written, a rational structure based on the same Γ-class was proposed by Katzarkov-Kontsevich-Pantev [53]b independently. We hope that an integral structure exists globally on the Ka¨hler moduli space ”
Matrix factorizations for nonaffine LG–models (2011, methodology): “This construction of matrix factorizations is also discussed in [ 5 ].”
A category of kernels for equivariant factorizations and its implications for Hodge theory (2011, background): “The Hochschild homology of C, HH∗(C), is an invariant that plays an important role in the noncommutative Hodge theory of C, [KKP08].”