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dc.contributor.advisorStarr, Jason M.en_US
dc.contributor.authorFindley, Robert Adamen_US
dc.contributor.otherDepartment of Mathematicsen_US
dc.date.accessioned2012-05-15T18:03:17Z
dc.date.available2012-05-15T18:03:17Z
dc.date.issued1-Dec-10en_US
dc.date.submittedDec-10en_US
dc.identifierFindley_grad.sunysb_0771E_10351.pdfen_US
dc.identifier.urihttp://hdl.handle.net/1951/55422
dc.description.abstractWe consider two properties of the Kontsevich moduli spaces of genus-0 stable maps to a variety X. The first, irreducibility, implies that certain genus-0 Gromov-Witten invariants are enumerative. The second, existence of very twisting families, implies the existence of sections for a two parameter family with vanishing elementary obstruction. Both of these properties are known to hold for homogeneous varieties, as well as low degree hypersurfaces in projective space.Motivated by these results for projective space, we prove that the Kontsevich moduli spaces are irreducible when X is a low degree hypersurface in a Grassmannian variety. We conjecture a sharp inequality kd^2 < n for when a two parameter family of degree $d$ hypersurfaces in the Grassmannian G(k,n) with vanishing elementary obstruction admits a rational section, and prove that a slightly weaker result holds.en_US
dc.description.sponsorshipStony Brook University Libraries. SBU Graduate School in Department of Mathematics. Lawrence Martin (Dean of Graduate School).en_US
dc.formatElectronic Resourceen_US
dc.language.isoen_USen_US
dc.publisherThe Graduate School, Stony Brook University: Stony Brook, NY.en_US
dc.subject.lcshMathematics.en_US
dc.subject.otherAlgebraic, Curves, Geometry, Grassmannian, Kontsevich, Rationalen_US
dc.titleRational Curves in Low Degree Hypersurfaces of Grassmannian Varietiesen_US
dc.typeDissertationen_US
dc.description.advisorAdvisor(s): Jason M. Starr. Committee Member(s): Dror Varolin; Aise J. de Jong; Samuel Grushevsky.en_US
dc.mimetypeApplication/PDFen_US


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