How to tell you're hearing a Calabi-Yau: Universal variations of Hodge structure and local Schottky relations for Calabi-Yau manifolds
A revised version with a number of corrections and refinements.
alg-geom↗
arXiv subjects
Ziv Ran
Publications and source records attributed to Ziv Ran.
On the local geometry of moduli spaces of vector bundles
We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of the bundle.
alg-geom↗
Thickening Calabi-Yau moduli spaces
We describe a kind of deformation of the anti-DeRham algebra on a Calabi-Yau manifold $X$. These are in 1-1 correspondence with the total cohomology $\oplus H^i (X, \C)$.
alg-geom↗
Lifting of cohomology and unobstructedness of certain holomorphic maps
Let $f$ be a holomorphic mapping between compact complex manifolds. We give a criterion for $f$ to have {\it unobstructed deformations}, i.e. for the local moduli space of $f$ to be smooth: this says, roughly speaking, that the group of infinitesimal deformations of $f$, when viewed as a functor, itself satisfies a natural lifting property with respect to infinitesimal deformations. This lifting property is satisfied e.g. whenever the group in question admits a `topological' or Hodge-theoretic interpretation, and we give a number of examples, mainly involving Calabi-Yau manifolds, where that is the case.
math.CV↗