6 papers
Generalized Bogomolov Inequalities
Mihai Pavel, Julius Ross, Matei Toma
We introduce the notion of a Hodge-Riemann pair of cohomology classes that generalizes the classical Hodge-Riemann bilinear relations, and the notion of a Bogomolov pair of cohomol…
Projectivity of Moduli Spaces in the Higher-Rank DT/PT Correspondence
Mihai Pavel, Tuomas Tajakka
We study projectivity of moduli spaces on the DT/PT wall crossing in Bridgeland and polynomial stability on a smooth, projective threefold. First, we construct a globally generated…
Slope-semistability and moduli of coherent sheaves: a survey
Mihai Pavel, Matei Toma
We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.
Moduli spaces of slope-semistable sheaves with reflexive Seshadri graduations
Mihai Pavel, Matei Toma
We study the moduli stacks of slope-semistable torsion-free coherent sheaves that admit reflexive, respectively locally free, Seshadri graduations on a smooth projective variety. W…
Uniform boundedness of semistable pure sheaves on projective manifolds
Mihai Pavel, Julius Ross, Matei Toma
We prove uniform boundedness statements for semistable pure sheaves on projective manifolds. For example, we prove that the set of isomorphism classes of pure sheaves of dimension…
Semistability conditions defined by ample classes
Damien Mégy, Mihai Pavel, Matei Toma
We study a class of semistability conditions defined by a system of ample classes for coherent sheaves over a smooth projective variety. Under some necessary boundedness assumption…