Landau-Ginzburg models -- old and new
arXiv:1405.2953
Abstract
In the last three years a new concept -- the concept of wall crossing has emerged. The current situation with wall crossing phenomena, after papers of Seiberg-Witten, Gaiotto-Moore-Neitzke, Vafa-Cecoti and seminal works by Donaldson-Thomas, Joyce-Song, Maulik-Nekrasov-Okounkov-Pandharipande, Douglas, Bridgeland, and Kontsevich-Soibelman, is very similar to the situation with Higgs Bundles after the works of Higgs and Hitchin -- it is clear that a general "Hodge type" of theory exists and needs to be developed. Nonabelian Hodge theory did lead to strong mathematical applications -- uniformization, Langlands program to mention a few. In the wall crossing is is also clear that some "Hodge type" of theory exists -- Stability Hodge Structure (SHS). This theory needs to be developed in order to reap some mathematical benefits --- solve long standing problems in algebraic geometry. In this paper we look at SHS from the perspective of Landau--Ginzburg models and we look at some applications. We consider simple examples and explain some conjectures these examples suggest.
arXiv comment29 pages; some references are added or updated
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Cited by in corpus (7)
- Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
- String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
- On deformations of toric Fano varieties
- Projecting Fanos in the mirror
- Laurent polynomials in Mirror Symmetry: why and how?
- Mutation equivalence of toric Landau-Ginzburg models
- SYZ for index 1 Fano hypersurfaces in projective space