Mathematics – Algebraic Geometry
Scientific paper
2007-09-14
Mathematics
Algebraic Geometry
92 pages, 1 figure; this version has more review of previous material and improved notation
Scientific paper
This paper continues the authors' program of studying mirror symmetry via log geometry and toric degenerations, relating affine manifolds with singularities, log Calabi-Yau spaces, and toric degenerations of Calabi-Yaus. The main focus of this paper is the calculation of the cohomology of a Calabi-Yau variety associated to a given affine manifold with singularities B. We show that the Dolbeault cohomology groups of the Calabi-Yau associated to B are described in terms of some cohomology groups of sheaves on B, as expected. This is proved first by calculating the log de Rham and log Dolbeault cohomology groups on the log Calabi-Yau space associated to B, and then proving a base-change theorem for cohomology in our logarithmic setting. As applications, this shows that our mirror symmetry construction via Legendre duality of affine manifolds results in the usual interchange of Hodge numbers expected in mirror symmetry, and gives an explicit description of the monodromy of a smoothing.
Gross Mark
Siebert Bernd
No associations
LandOfFree
Mirror Symmetry via Logarithmic Degeneration Data II 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 Mirror Symmetry via Logarithmic Degeneration Data II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mirror Symmetry via Logarithmic Degeneration Data II will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-616447