科研之友
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摘要
In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Bogomolov Tian-Todorov theorem for the deformations of Landau Ginzburg models, develop the necessary Hodge theory for varieties with potentials, and prove a double degeneration statement needed for the unobstructedness result. We discuss the various definitions of Hodge numbers for non-commutative Hodge structures of Landau Ginzburg type and the role they play in mirror symmetry. We also interpret the resulting families of de Rham complexes attracted to a potential in terms of mirror symmetry for one parameter families of symplectic Fano manifolds and argue that modulo a natural triviality property the moduli spaces of Landau Ginzburg models posses canonical special coordinates.
- 出版日期2017-1
