4 papers
Numerical contraction for orbifold surfaces
Nathan Grieve
We study singularities and Artin's contraction theorem for orbifold surfaces. Our main result has a consequence which is in the direction of the birational Minimal Model Program fo…
Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles
Nathan Grieve
We study the property of \emph{continuous Castelnuovo-Mumford regularity}, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in \cite{Kuronya:Mu…
Generalized GCD for toric Fano varieties
Nathan Grieve
We study the greatest common divisor problem for torus invariant blowing-up morphisms of nonsingular toric Fano varieties. Our main result applies the theory of Okounkov bodies tog…
Divisorial instability and Vojta's Main Conjecture for -Fano varieties
Nathan Grieve
We study Diophantine arithmetic properties of birational divisors in conjunction with concepts that surround -stability for Fano varieties. There is also an interpretat…