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Regular version of the site

Book chapter

Birational geometry via moduli spaces

P. 93-132.
In this paper we connect degenerations of Fano threefolds by projections. Using mirror symmetry we transfer these connections to the side of Landau–Ginzburg models. Based on that we suggest a generalization of Kawamata’s categorical approach to birational geometry enhancing it via geometry of moduli spaces of Landau–Ginzburg models. We suggest a conjectural application to the Hassett–Kuznetsov–Tschinkel program, based on new nonrationality “invariants”—gaps and phantom categories. We formulate several conjectures about these invariants in the case of surfaces of general type and quadric bundles.

In book

Edited by: F. A. Bogomolov, B. Hasset, Y. Tschinkel. Boston: Birkhäuser, 2013.