4 papers
Moduli of non-pure sheaves and contractions of Hilbert schemes
Andres Fernandez Herrero, Svetlana Makarova
We define certain stacks of rank one sheaves on a smooth projective variety, and show that they admit proper good moduli spaces. We offer several applications to contractions of su…
There are no exotic compact moduli of sheaves on a curve
Andres Fernandez Herrero, Dario Weissmann, Xucheng Zhang
We study moduli of coherent sheaves of some given degree and positive rank on a curve. We show that there is only one nonempty open condition on families of sheaves that yields a u…
Distinguishing Algebraic Spaces from Schemes
Andres Fernandez Herrero, Dario Weißmann, Xucheng Zhang
We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to d…
Moduli of objects in finite length abelian categories
Andres Fernandez Herrero, Emmett Lennen, Svetlana Makarova
We construct moduli spaces of objects in an abelian category satisfying some finiteness hypotheses. Our approach is based on the work of Artin-Zhang and the intrinsic construction…