Gromov-Witten correspondences, derived categories, and Frobenius manifolds
Gromov-Witten correspondences, derived categories, and Frobenius manifolds
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dc.contributor.advisor | Manin, Yuri I. | |
dc.contributor.author | Smirnov, Maxim | |
dc.date.accessioned | 2020-04-18T17:16:25Z | |
dc.date.available | 2020-04-18T17:16:25Z | |
dc.date.issued | 21.02.2013 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/5627 | |
dc.description.abstract | 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. | |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Gromov-Witten correspondences, derived categories, and Frobenius manifolds | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5n-31252 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 3125 | |
ulbbnediss.date.accepted | 23.01.2013 | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Huybrechts, Daniel |
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