Cohomology and Obstructions III: A variational form of the generalized Hodge conjecture on K-trivial threefolds

Details Cohomology and Obstructions III: A variational form of the generalized Hodge conjecture on K-trivial threefolds Cohomology and Obstructions III: A variational form of the generalized Hodge conjecture on K-trivial threefolds

1998-09-22

arxiv.org/abs/math/9809127v4

Mathematics

Algebraic Geometry

23 pages, latex2e file, correction of previous version entitled "Cohomology and Obstructions II: Curves on Calabi-Yau threefol

Scientific paper

This paper studies the Hilbert scheme of a curve on a complete-intersection K-trivial threefold, in the case in which the curve is unobstructed in the ambient variety in which the threefold lives. The basic result is that the obstruction theory of the curve is completely determined by the scheme-theoretic Abel-Jacobi mapping. Several applications of this fact are given.

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