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Moduli schemes associated to  -trivial threefolds as gradient schemes
Author(s):
Herb
Clemens
Journal:
J. Algebraic Geom.
14
(2005),
705-739.
Posted:
May 12, 2005
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Abstract |
References |
Additional information
Abstract:
On a threefold with trivial canonical bundle, Kuranishi theory gives an algebro-geometry construction of the (local analytic) Hilbert scheme of curves at a smooth holomorphic curve as a gradient scheme, that is, the zero-scheme of the exterior derivative of a holomorphic function on a (finite-dimensional) polydisk. (The corresponding fact in an infinite-dimensional setting was long ago discovered by physicists.) This parallels the way the holomorphic Chern-Simons functional gives the local analytic moduli scheme for vector bundles on a Calabi-Yau threefold. An analogous gradient scheme construction for Noether-Lefschetz loci on ample divisors is also given. Finally, using a structure theorem of Donagi-Markman, we present a new formulation of the Abel-Jacobi mapping into the intermediate Jacobian of a threefold with trivial canonical bundle.
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Additional Information:
Herb
Clemens
Affiliation:
Mathematics Department, Ohio State University, 231 W. 18th Ave., Columbus, Ohio 43210
Email:
clemens@math.ohio-state.edu
PII:
S 1056-3911(05)00413-3
Received by editor(s):
August 26, 2004
Received by editor(s) in revised form:
February 28, 2005 and March 17, 2005
Posted:
May 12, 2005
Additional Notes:
Partially supported by NSF grant DMS-0200895
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