Duke Mathematical Journal
- Duke Math. J.
- Volume 161, Number 5 (2012), 803-843.
Symplectic geometry of rationally connected threefolds
We study the symplectic geometry of rationally connected -folds. The first result shows that rational connectedness is a symplectic deformation invariant in dimension . If a rationally connected -fold is Fano or has Picard number , we prove that there is a nonzero Gromov–Witten invariant with two insertions being the class of a point. That is, is symplectic rationally connected. Finally we prove that many rationally connected -folds are birational to a symplectic rationally connected variety.
Duke Math. J., Volume 161, Number 5 (2012), 803-843.
First available in Project Euclid: 27 March 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14M22: Rationally connected varieties 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
Tian, Zhiyu. Symplectic geometry of rationally connected threefolds. Duke Math. J. 161 (2012), no. 5, 803--843. doi:10.1215/00127094-1548398. https://projecteuclid.org/euclid.dmj/1332866804