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Finiteness of open substacks with proper moduli spaces
Xucheng Zhang
For an algebraic stack of finite type, we construct a finite stratification of an atlas such that every universally closed open substack pulls back to a union of strata. As a resul…
Open substacks preserving moduli spaces: classification and bounds
Jianping Wang, Xucheng Zhang
For a smooth locally reductive stack admitting an adequate moduli space, we show that there are finitely many open substacks preserving the adequate moduli space, and give a comple…
Comparing local-global obstructions on algebraic stacks
Chang Lv, Han Wu, Xucheng Zhang
Let k be a number field. For quotient stacks [X/G] with X a smooth quasi-projective geometrically integral k-variety and G a linear k-group, we extend several relations between loc…
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…
S-equivalence for algebraic stacks
Xucheng Zhang
We generalize the notion of S-equivalence, previously defined for semistable vector bundles, to points in arbitrary algebraic stacks and use it to describe the identification of po…
Proper good quotients for -actions
Xucheng Zhang
We give an algebraic proof of a result, due to Bialynicki-Birula and Sommese, characterizing the invariant open subsets of a normal proper variety equipped with a -ac…
On the moment measure conjecture
Jochen Heinloth, Xucheng Zhang
The moment measure conjecture of Bialynicki-Birula and Sommese gives a combinatorial characterization of all open substacks of a global quotient stack for a torus action on a norma…
A stacky approach to identifying the semistable locus of bundles
Dario Weissmann, Xucheng Zhang
We show that the semistable locus is the unique maximal open substack of the moduli stack of principal bundles over a curve that admits a schematic moduli space. For rank vecto…