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arXiv · 1405.3374

Birational geometry via moduli spaces

Ivan Cheltsov·Ludmil Katzarkov·Victor Przyjalkowski
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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 Hasset--Kuznetsov--Tschinkel program based on new nonrationality "invariants" we consider --- gaps and phantom categories. We make several conjectures for these invariants in the case of surfaces of general type and quadric bundles.

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Ivan Cheltsov, Ludmil Katzarkov, Victor Przyjalkowski. 2014-05-14. Birational geometry via moduli spaces. https://arxiv.org/abs/1405.3374

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