Symplectic geometry of rationally connected threefolds. (English) Zbl 1244.14041

Tian, Zhiyu

Duke Math. J. 161, No. 5, 803-843 (2012).

This paper mainly concerns the following conjecture of J. Kollár [Prog. Math. 168, 255–288 (1998; Zbl 0970.14001)]: Let \(X\) and \(X'\) be two smooth projective varieties which are symplectic deformation equivalent. Then \(X\) is rationally connected if and only if \(X'\) is. The author proved Kollár’s conjecture in dimension \(3\) by using the strategy of C. Voisson [Astérisque 322, 1–21 (2008; Zbl 1178.14048)]. An important ingredient is the proof of existence of nonzero Gromov-Witten invariants in genus zero.

Reviewer: Hao Xu (Cambridge)

MSC:

14M22	Rationally connected varieties
14N35	Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)

Keywords:

rationally connected; Gromov-Witten invariants

Citations:

Zbl 0970.14001; Zbl 1178.14048

References:

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