Birational Geometry via Moduli Spaces

Ivan Cheltsov (), Ludmil Katzarkov () and Victor Przyjalkowski ()
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Ivan Cheltsov: University of Edinburgh
Ludmil Katzarkov: University of Miami
Victor Przyjalkowski: Steklov Mathematical Institute

A chapter in Birational Geometry, Rational Curves, and Arithmetic, 2013, pp 93-132 from Springer

Abstract: 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.

Keywords: Modulus Space; Pezzo Surface; Smooth Point; Higgs Bundle; Fano Variety (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-6482-2_5

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

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