Generic Deformations of Varieties

Deformations of Aane Torus Varieties

Algebraic Deformations of Polarized Varieties

Introduction. Let F b e a projectively embeddable complete non-singular variety of dimension n > 1 . Let f be a projective embedding of 7, U a nonsingular variety, W a non-singular variety and φ a morphism of W onto U such that φ^iuo) = f{V) for some point u0 of U. Denote by ΣffO the set of all those complete non-singular fibres φ~(u), u e ί/, as we consider all possible (f, U, W). Suppose that...

Jumping deformations of complete toric varieties

We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under some assumptions, the general fibers of these families also become toric varieties and we can explicitly describe the corresponding fans from the data of the fans corresponding to the special fibers. Using these families, we give a deformation family for a certain toric weakened Fano 3-...

Poisson deformations of affine symplectic varieties II

Let Y be an affine symplectic variety of dimension 2n, and let π : X → Y be a crepant resolution. By the definition, there is a symplectic 2-form σ̄ on the smooth part Yreg ∼= π (Yreg), and it extends to a 2-form σ on X. Since π is crepant, σ is a symplectic 2-form on X. The symplectic structures on X and Y define Poisson structures on them in a natural manner. One can define a Poisson deformati...

On deformations of Q-factorial symplectic varieties

This is a supplement to [Na]. In [Na] we have proposed a new category of complex symplectic varieties which admit certain singularities. It includes symplectic V-manifolds (cf. [Fu]) and O’Grady’s singular moduli spaces of semi-stable torsion free sheaves on a K3 surface [O] (cf. [Na], Introduction). A normal compact Kahler space Z is a symplectic variety if its regular locus U admits a non-deg...