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.
CITATION STYLE
Cheltsov, I., Katzarkov, L., & Przyjalkowski, V. (2013). Birational geometry via moduli spaces. In Birational Geometry, Rational Curves, and Arithmetic (pp. 93–132). Springer New York. https://doi.org/10.1007/978-1-4614-6482-2_5
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