Several Complex Variables
John Horvath, "Several Complex Variables"
1971 | pages: 290 | ISBN: 3540053727, 0387053727 | PDF | 7,8 mb
1971 | pages: 290 | ISBN: 3540053727, 0387053727 | PDF | 7,8 mb
The algebraic cycles which lie in a smooth, projective algebraic variety, together with the various equivalence relations (such as numerical or algebraic equivalence) which may be defined on such cycles, constitute a purely algebro-geometric concept. One may, however, attempt to study these by transcendental methods, and historically much of the structure of algebraic cycles (such as the notion of linear equivalence of divisors as related to the Jacobian and Picard varieties) was discovered in this way. Conversely, the questions in complex function theory which arose initially from algebraic geometry are frequently quite interesting in themselves. For example, the irst and second Cousin problems for divisors in <Cn were very much motivated by consideration of the Jacobian varieties of curves.
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