Abstract
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.
Original language | English (US) |
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Title of host publication | Birational Geometry, Rational Curves, and Arithmetic |
Publisher | Springer New York |
Pages | 93-132 |
Number of pages | 40 |
ISBN (Electronic) | 9781461464822 |
ISBN (Print) | 9781461464815 |
DOIs | |
State | Published - Jan 1 2013 |
ASJC Scopus subject areas
- Mathematics(all)