Type
Text
Type
Dissertation
Advisor
Aleksey Zinger | Jason M. Starr. | Radu Laza | Dusa McDuff.
Date
2011-05-01
Keywords
birational geometry, Gromov-Witten invariant, rationally connected variety, symplectic geometry | 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/11401/71714
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We study the symplectic geometry of rationally connected 3-folds. The first result shows that rational connectedness is a symplectic deformation invariant in dimension 3. If a rationally connected 3-fold X is Fano or has Picard number 2, we prove that there is a non-zero Gromov-Witten invariant with two insertions being the class of a point. Finally we prove that many other rationally connected 3-folds have birational models admitting a non-zero Gromov-Witten invariant with two point insertions.
Recommended Citation
Tian, Zhiyu, "Symplectic geometry of rationally connected threefolds" (2011). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 919.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/919