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Surgery, quantum cohomology and birational geometry. (English) Zbl 0952.53001
Eliashberg, Ya. (ed.) et al., Northern California symplectic geometry seminar. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 196(45), 183-198 (1999).
The paper under review is a survey about quantum cohomology and birational geometry.
The material is organized as follows: In Section 2, the author gives a brief introduction to quantum cohomology and the naturality problem. Sections 3 and 4 deal with Mori’s minimal model program and, respectively, with the connection between the naturality problem and birational geometry. Finally, in Section 5, some open problems are nicely pointed out.
In conclusion, a very nice paper.
For the entire collection see [Zbl 0930.00050].

MSC:
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
14E30 Minimal model program (Mori theory, extremal rays)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
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