Rocky Mountain Journal of Mathematics

Welschinger invariants of blow-ups of symplectic 4-manifolds

Yanqiao Ding and Jianxun Hu

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Using the degeneration technique, we study the behavior of Welschinger invariants under the blow-up and obtain some blow-up formulae of Welschinger invariants. To analyze the variation of Welschinger invariants when replacing a pair of real points in the real configuration by a pair of conjugated points, Welschinger introduced the $\theta $-invariant. In this paper, we also verify that the $\theta $-invariant is the Welschinger invariant of the blow-up of the symplectic $4$-manifold.

Article information

Rocky Mountain J. Math., Volume 48, Number 4 (2018), 1105-1144.

First available in Project Euclid: 30 September 2018

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Zentralblatt MATH identifier

Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
Secondary: 14N05: Projective techniques [See also 51N35] 14N10: Enumerative problems (combinatorial problems) 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45] 14P25: Topology of real algebraic varieties

Real symplectic blow-up Welschinger invariants blow-up formula real enumerative geometry


Ding, Yanqiao; Hu, Jianxun. Welschinger invariants of blow-ups of symplectic 4-manifolds. Rocky Mountain J. Math. 48 (2018), no. 4, 1105--1144. doi:10.1216/RMJ-2018-48-4-1105.

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