Non-quasi-projective moduli spaces

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...

Non – Quasi – Projective

Moduli Spaces of Twisted Sheaves on a Projective Variety

Let X be a smooth projective variety over C. Let α := {αijk ∈ H(Ui ∩ Uj ∩ Uk,O X)} be a 2-cocycle representing a torsion class [α] ∈ H2(X,O X). An α-twisted sheaf E := {(Ei, φij)} is a collection of sheaves Ei on Ui and isomorphisms φij : Ei|Ui∩Uj → Ej|Ui∩Uj such that φii = idEi , φji = φ ij and φki ◦ φjk ◦ φij = αijk idEi . We assume that there is a locally free α-twisted sheaf, that is, α giv...

Projective Toric Varieties as Fine Moduli Spaces of Quiver Representations

This paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver. To accomplish this, we study the quiver Q with relations R corresponding to the finite-dimensional algebra End (⊕ r i=0 Li ) where L := (OX , L1, . . . , Lr) is a list of line bundles on a projective toric variety X . The quiver Q defines a unimodular, projec...

Quasi-projectivity of Moduli Spaces of Polarized Varieties

By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of non-uniruled polarized varieties.