Type
Text
Type
Dissertation
Advisor
Dror Varolin | Starr, Jason M. | Aise J. de Jong | Samuel Grushevsky.
Date
2010-12-01
Keywords
Algebraic, Curves, Geometry, Grassmannian, Kontsevich, Rational | Mathematics.
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/70987
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
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.
Recommended Citation
Findley, Robert Adam, "Rational Curves in Low Degree Hypersurfaces of Grassmannian Varieties" (2010). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 195.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/195