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Lectures on Hodge Theory and Algebraic Cycles

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Lectures on Hodge Theory and Algebraic Cycles

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Abstract

Notes for a mini course at the University of Science and Technology of China in Hefei, China, June 23–July 12, 2014.

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... The following theorem comprise certain results of [357,358] for the case of Fano complete intersections of index 1. See, e.g., [57,315,314,357,358,359,427,507,552] and the literature therein for the cylinder mappings on cycles of other intermediate dimensions. See also [49] on the intermediate jacobians of conic bundles. ...
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This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.
... Of course, this is a known fact in view of Theorem 2.3. [Le2,As] ...
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