We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the e-print archive: http://xxx.lanl.gov/hep-th/9903053 2 "Convex" means that H 1 (C, f*V)=0 for (C, /) .Mo,o (d; P). For the simplest example, P = P 4 and V = 0(5), as in the next subsection.
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Chiang et al. (1999) studied this question.
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