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  Gromov-Witten correspondences, derived categories, and Frobenius manifolds

Smirnov, M. (2013). Gromov-Witten correspondences, derived categories, and Frobenius manifolds. PhD Thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn.

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Datensatz-Permalink: https://hdl.handle.net/21.11116/0000-0004-1CA8-0 Versions-Permalink: https://hdl.handle.net/21.11116/0000-0009-0176-1
Genre: Hochschulschrift

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https://hdl.handle.net/20.500.11811/5627 (beliebiger Volltext)
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 Urheber:
Smirnov, Maxim1, Autor           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Zusammenfassung: In this thesis we consider questions arising in Gromov-Witten theory, quantum cohomology and mirror symmetry. The first two chapters deal with Gromov-Witten theory and derived categories for moduli spaces of stable curves of genus zero with n marked points. In the third chapter we consider Landau-Ginzburg models for odd-dimensional quadrics.
In the first chapter we study moduli spaces of stable maps with target being the moduli space of stable curves of genus zero with n marked points, and curve class being a class of a boundary curve. An explicit formula for the respective Gromov-Witten invariants is given.
In the second chapter we consider inductive constructions of semi-orthogonal decompositions and exceptional collections in the derived category of moduli spaces moduli spaces of stable curves of genus zero with n marked points based on a nice presentation of these spaces as consecutive blow-ups due to Keel.
In the third chapter we give an ad hoc partial compactification of the standard Landau-Ginzburg potential for an odd-dimensional quadric, and study its Gauss-Manin system in the case of three dimensional quadrics. We show that under some hypothesis this Landau-Ginzburg potential would give a Frobenius manifold isomorphic to the quantum cohomology of a three dimensional quadric.

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Sprache(n): eng - English
 Datum: 2013
 Publikationsstatus: Angenommen
 Seiten: I, 77 p.
 Ort, Verlag, Ausgabe: Bonn : Rheinische Friedrich-Wilhelms-Universität Bonn
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: URN: https://nbn-resolving.org/urn:nbn:de:hbz:5n-31252
 Art des Abschluß: Doktorarbeit

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