ﻻ يوجد ملخص باللغة العربية
In this paper, Gotzmanns Regularity Theorem is established for globally generated coherent sheaves on projective space. This is used to extend Gotzmanns explicit construction to the Quot scheme. The Gotzmann representation is applied to bound the second Chern class of a rank 2 globally generated coherent sheaf in terms of the first Chern class.
In algebraic geometry, one often encounters the following problem: given a scheme X, find a proper birational morphism from Y to X where the geometry of Y is nicer than that of X. One version of this problem, first studied by Faltings, requires Y to
We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of arithmetic local Langlands parameters, including their roles played in the local-global compatibility in the Langlands program. We survey some known results as evidences of these conjectures.
Let $X$ be a compact Calabi-Yau 3-fold, and write $mathcal M,bar{mathcal M}$ for the moduli stacks of objects in coh$(X),D^b$coh$(X)$. There are natural line bundles $K_{mathcal M}tomathcal M$, $K_{bar{mathcal M}}tobar{mathcal M}$, analogues of canon
We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber) in the co
The aim of these notes is to generalize Laumons construction [18] of automorphic sheaves corresponding to local systems on a smooth, projective curve $C$ to the case of local systems with indecomposable unipotent ramification at a finite set of point