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Rational Curves in Low Degree Hypersurfaces of Grassmannian Varieties

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dc.contributor.advisor Starr, Jason M. en_US
dc.contributor.author Findley, Robert Adam en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2012-05-15T18:03:17Z
dc.date.accessioned 2015-04-24T14:45:25Z
dc.date.available 2012-05-15T18:03:17Z
dc.date.available 2015-04-24T14:45:25Z
dc.date.issued 2010-12-01 en_US
dc.identifier Findley_grad.sunysb_0771E_10351.pdf en_US
dc.identifier.uri http://hdl.handle.net/1951/55422 en_US
dc.identifier.uri http://hdl.handle.net/11401/70987 en_US
dc.description.abstract We 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.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics. en_US
dc.subject.other Algebraic, Curves, Geometry, Grassmannian, Kontsevich, Rational en_US
dc.title Rational Curves in Low Degree Hypersurfaces of Grassmannian Varieties en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Dror Varolin en_US
dc.contributor.committeemember Aise J. de Jong en_US
dc.contributor.committeemember Samuel Grushevsky. en_US

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