Birational geometry via moduli spaces

Ivan Cheltsov, Ludmil Katzarkov, Victor Przyjalkowski

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationBirational Geometry, Rational Curves, and Arithmetic
PublisherSpringer New York
Pages93-132
Number of pages40
ISBN (Electronic)9781461464822
ISBN (Print)9781461464815
DOIs
StatePublished - Jan 1 2013

ASJC Scopus subject areas

  • Mathematics(all)

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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