Log-terminal singularities and vanishing theorems via non-standard tight closure

Log-terminal Singularities and Vanishing Theorems via Non-standard Tight Closure

Generalizing work of Smith and Hara, we give a new characterization of logterminal singularities for finitely generated algebras over C, in terms of purity properties of ultraproducts of characteristic p Frobenii. As a first application we obtain a Boutot-type theorem for log-terminal singularities: given a pure morphism Y → X between affine Q-Gorenstein varieties of finite type over C, if Y ha...

Tight Closure and the Kodaira Vanishing Theorem

Non-standard tight closure for affine C-algebras

In this paper, non-standard tight closure is proposed as an alternative for classical tight closure on finitely generated algebras over C. It has the advantage that it admits a functional definition, similar to the characteristic p definition of tight closure, where instead of the characteristic p Frobenius, its ultraproduct, the non-standard Frobenius, is used. This new closure operation cl(·)...

The Vanishing Neighbourhood of Non-isolated Singularities

We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles. For one dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy via monodromies of n...

Vanishing theorems for Dolbeault cohomology of log homogeneous varieties

We consider a complete nonsingular variety X over C, having a normal crossing divisor D such that the associated logarithmic tangent bundle is generated by its global sections. We show that H (