Hodge sheaves underlying flat projective families

K-FLAT PROJECTIVE FUZZY QUANTALES

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

Flat Projective Connections

Ample Sheaves and Ample Families

1 Ample Sheaves Let X be a scheme and L an invertible sheaf. Given a global section f ∈ Γ(X,L ) the set Xf = {x ∈ X | germxf / ∈ mxLx} is open (MOS,Lemma 29). The inclusion Xf −→ X is affine (RAS,Lemma 6) and in particular if X is an affine scheme then Xf is itself affine. Given a sequence of global sections f1, . . . , fn the open sets Xfi cover X if and only if the fi generate L (MOS,Lemma 32...

Instanton sheaves on complex projective spaces

We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of modu...

Koszul Algebras and Sheaves over Projective Space

We are going to show that the sheafication of graded Koszul modules KΓ over Γn = K [x0, x1...xn] form an important subcategory ∧ KΓ of the coherents sheaves on projective space, Coh(P n). One reason is that any coherent sheave over P n belongs to ∧ KΓup to shift. More importantly, the category KΓ allows a concept of almost split sequence obtained by exploiting Koszul duality between graded Kosz...