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Birational Geometry via Moduli Spaces

In: Birational Geometry, Rational Curves, and Arithmetic

Author

Listed:
  • Ivan Cheltsov

    (University of Edinburgh)

  • Ludmil Katzarkov

    (University of Miami
    University of Vienna)

  • Victor Przyjalkowski

    (Steklov Mathematical Institute)

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.

Suggested Citation

  • Ivan Cheltsov & Ludmil Katzarkov & Victor Przyjalkowski, 2013. "Birational Geometry via Moduli Spaces," Springer Books, in: Fedor Bogomolov & Brendan Hassett & Yuri Tschinkel (ed.), Birational Geometry, Rational Curves, and Arithmetic, edition 127, pages 93-132, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-6482-2_5
    DOI: 10.1007/978-1-4614-6482-2_5
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