Framed sheaves on projective stacks

Moduli spaces of framed instanton sheaves on projective spaces

We introduce a generalization of the Atiyah-Drinfeld-Hitchin-Manin linear algebraic data and a generalization of Atiyah-Drinfeld-Hitchin-Manin equation, which are subsequently used to construct all framed instanton bundles on complex projective spaces. Using geometric invariant theory, we prove that the moduli spaces of framed instanton sheaves is a quasiprojective variety. We also provide a li...

Representability for Some Moduli Stacks of Framed Sheaves

We prove that certain moduli functors (and stacks) for framed torsion-free sheaves on complex projective surfaces are represented by schemes.

Sheaves on Artin Stacks

We develop a theory of quasi–coherent and constructible sheaves on algebraic stacks correcting a mistake in the recent book of Laumon and Moret-Bailly. We study basic cohomological properties of such sheaves, and prove stack–theoretic versions of Grothendieck’s Fundamental Theorem for proper morphisms, Grothendieck’s Existence Theorem, Zariski’s Connectedness Theorem, as well as finiteness Theo...

Sheaves on Algebraic Stacks

Sheaves on Algebraic Stacks