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	New Construction of Complex Manifold via Conifold Transition
	Xu, Jin Xing
	2012
关键词	Calabi-Yau threefolds conifold transitions complex structures on connected sums of S-3 x S-3 CALABI-YAU THREEFOLDS RATIONAL CURVES CLASSIFICATION
英文摘要	For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds which is diffeomorphic to connected sums of S-3 x S-3. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S-3 x S-3. This construction is an analogue of that made by Friedman [On threefolds with trivial canonical bundle. In: Complex Geometry and Lie Theory, volume 53 of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1991, 103-134], Lu and Tian [Complex structures on connected sums of S-3 x S-3. In: Manifolds and Geometry, Pisa, 1993, 284-293] who used only quintics in P-4.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000305045100004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; Mathematics; SCI(E); 中国科技核心期刊(ISTIC); 中国科学引文数据库(CSCD); 0; ARTICLE; 7; 1347-1368; 28
语种	英语
出处	SCI
出版者	acta mathematica sinica english series
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157536]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xu, Jin Xing. New Construction of Complex Manifold via Conifold Transition. 2012-01-01.

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