A Generalization of Curve Genus for Ample Vector Bundles, I
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چکیده
A new genus g = g(X, E) is defined for the pairs (X, E) that consist of n-dimensional compact complex manifolds X and ample vector bundles E of rank r less than n on X. In case r = n − 1, g is equal to curve genus. Above pairs (X,E) with g less than two are classified. For spanned E it is shown that g is greater than or equal to the irregularity of X, and its equality condition is given.
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تاریخ انتشار 2008