Deformations of Landau-Ginzburg models, I


13:00:00 - 14:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In these two talks, we follow the method in [1] to prove, a specific deformation problem of a compactified Landau-Ginzburg model Z is unobstructed (under a tameness condition). We first fix settings and form the deformation problem. Then, we introduce the sheaf of f-adapted forms and give an outline of the proof. After this, and in the second talk, we develop the knowledge of the involved technical tools in the proof - the DGLA and the L-infinity algebra.
[1] L.Katzarkov, M.Kontsevich and T.Pantev, Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models.
[2] Marco Manetti, Deformation theory via differential graded Lie algebras.
[3] Seminari di Geometria Algebrica, 1998-1999.
[4] Domenico Fiorenza, Donatella Iacono and Elena Martinengo, Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves.
[5] X.Z. Cheng and E. Getzler, Homotopy commutative algebraic structures.