Symplectic Geometry and Mirror Symmetry,: Proceedings of the by Y.G. Oh, K. Fukaya, Y-G Oh, K. Ono, G. Tian

By Y.G. Oh, K. Fukaya, Y-G Oh, K. Ono, G. Tian

Complaints of the 4th KIAS Annual foreign convention, held in August 14-18, 2000, Seoul, South Korea. best specialists within the box discover the newer advancements with regards to homological replicate symmetry, Floer thought, D-branes and Gromov-Witten invariants.

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4. D. Auroux, Symplectic maps to projective spaces and symplectic invariants, to appear in Proc. 7th Gokova Geometry-Topology Conference (2000), International Press. 5. D. Auroux, L. Katzarkov, Branched coverings of GP 2 and invariants of symplectic 4-manifolds, to appear in Invent. Math. 6. J. M. Boardman, Singularities of differentiate maps, Publ. Math. IHES, 33 (1967), 21-57. 7. S. K. Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996), 666-705. 8.

Consequently, the charge vector £(*"> for the fiber is the same and there is a simple change in the charge vector (SB) for the base. The difference of the curve of the B-model appears only in the last term with coefficient 04. ^B\ the identification of the moduli ZB is also changed. ; 0,1,-1,1). 4) gives Y = {sx;x\z,s% 2 x s ). 4X . (B> = ( - 2 ; 0 , 1 , 0 , 1 ) . 4) is solved by 2 2 F=(sx;x2,z,s2,—) . 20) y2 = (aix2 + a0x + a3)2 - 4a 2 a 4 x 2 . ' B a2a4 K4 * =^r =^ • (A 24) - for F 0 . Finally we make a comparison of differential operators of GKZ.

The limit £# —¥ 00 may also be regarded as the limit of shrinking F n with the size of the fiber being kept fixed. Previously it was pointed out that the amplitudes of the string theory compactified on local models F n with n = 0,1,2 all give the same results in the R —> 0 limit and reduce to the Seiberg-Witten solution 7 . What we would like to emphasize in this paper is that only the F 2 model has the correct behavior in the opposite limit R —> 00 and reproduce the known result. We 31 32 thus propose the low energy effective action based on the local F2 as the exact solution of 5-dimensional SU(2) gauge theory on R4 x S 1 for any radius R.

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