Birational geometry via moduli spaces

Ivan Cheltsov; Ludmil Katzarkov; Victor Przyjalkowski

doi:10.1007/978-1-4614-6482-2_5

Birational geometry via moduli spaces

Ivan Cheltsov, Ludmil Katzarkov, Victor Przyjalkowski

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

7 Scopus citations

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)
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	https://doi.org/10.1007/978-1-4614-6482-2_5
State	Published - Jan 1 2013

ASJC Scopus subject areas

Mathematics(all)

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10.1007/978-1-4614-6482-2_5

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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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