Cubics, Integrable Systems, and Calabi-Yau Threefolds

Details Cubics, Integrable Systems, and Calabi-Yau Threefolds Cubics, Integrable Systems, and Calabi-Yau Threefolds

1994-08-09

arxiv.org/abs/alg-geom/9408004v1

Mathematics

Algebraic Geometry

28 p., Latex

Scientific paper

In this work we construct an analytically completely integrable Hamiltonian system which is canonically associated to any family of Calabi-Yau threefolds. The base of this system is a moduli space of gauged Calabi-Yaus in the family, and the fibers are Deligne cohomology groups (or intermediate Jacobians) of the threefolds. This system has several interesting properties: the multivalued sections obtained as Abel-Jacobi images, or ``normal functions'', of a family of curves on the generic variety of the family, are always Lagrangian; the natural affine coordinates on the base, which are used in the mirror correspondence, arise as action variables for the integrable system; and the Yukawa cubic, expressing the infinitesimal variation of Hodge structure in the family, is essentially equivalent to the symplectic structure on the total space.

Affiliated with

Also associated with

No associations

Rating

Cubics, Integrable Systems, and Calabi-Yau Threefolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cubics, Integrable Systems, and Calabi-Yau Threefolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cubics, Integrable Systems, and Calabi-Yau Threefolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-194473