Duke Mathematical Journal

Symplectic geometry of rationally connected threefolds

Zhiyu Tian

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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 nonzero Gromov–Witten invariant with two insertions being the class of a point. That is, X is symplectic rationally connected. Finally we prove that many rationally connected 3-folds are birational to a symplectic rationally connected variety.

Article information

Duke Math. J., Volume 161, Number 5 (2012), 803-843.

First available in Project Euclid: 27 March 2012

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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

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