It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.
In this article we prove that every entire curve in a generic hypersurface of degree in is algebraically degenerated i.e there exists a proper subvariety which contains the entire curve.
We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so-called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient is weakly proper and if in addition the quotient variety is of expected dimension then the toric quotient is a categorical quotient in the category of algebraic varieties. For example, weak properness always holds for the toric quotient of a subtorus action...
A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.