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OverviewPlease note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. High Quality Content by WIKIPEDIA articles! In algebraic geometry, a branch of mathematics, the Lefschetz theorem on (1,1)-classes, named after Solomon Lefschetz, is a classical statement relating divisors on a compact Kahler manifold to classes in its integral cohomology. It is the only case of the Hodge conjecture which has been proved for all Kahler manifolds.Let X be a compact Kahler manifold. There is a cycle class map that takes a divisor class to a cohomology class. In this case, it is the first Chern class c1 from linear equivalence classes of divisors to H2(X, Z). By Hodge theory, the de Rham cohomology group H2(X, C) decomposes as a direct sum H0,2(X) ae* H1,1(X) ae* H2,0(X), and it can be proved that the image of the cycle class map lies in H1,1(X). The theorem says that the map to H2(X, Z) ae(c) H1,1(X) is surjective. Full Product DetailsAuthor: Lambert M. Surhone , Miriam T. Timpledon , Susan F. MarsekenPublisher: VDM Publishing House Imprint: VDM Publishing House Dimensions: Width: 22.90cm , Height: 0.50cm , Length: 15.20cm Weight: 0.142kg ISBN: 9786131201639ISBN 10: 6131201633 Pages: 88 Publication Date: 12 August 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |