Mongodi, Samuele Tomassini, Giuseppe
Published in
Bollettino dell'Unione Matematica Italiana

The name of Oka principle, or Oka–Grauert principle, is traditionally used to refer to the holomorphic incarnation of the homotopy principle: on a Stein space, every problem that can be solved in the continuous category, can be solved in the holomorphic category as well. In this note, we begin the study of the same kind of questions on a Levi-flat ...

Maslovarić, Marcel Seppänen, Henrik
Published in
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

We generalize the notion of multi-Gieseker semistability for coherent sheaves, introduced by Greb, Ross, and Toma, to quiver sheaves for a quiver Q. We construct coarse moduli spaces for semistable quiver sheaves using a functorial method that realizes these as subschemes of moduli spaces of representations of a twisted quiver, depending on Q, with...

Zheng, Weizhe
Published in
Mathematische Zeitschrift

Deligne’s conjecture that ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-adic sheaves on normal schemes over a finite field admit ℓ′\documentcla...

Maican, Mario
Published in
Geometriae Dedicata

We study the moduli spaces of stable sheaves of Euler characteristic 1, respectively 2, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that these moduli spaces are rational. We give a classification of the stable sheaves involving locally free resolutions or extensions. We find a global description of the f...

Zhuang, Xiaobo
Published in
Frontiers of Mathematics in China

By using the Bialynicki-Birula decomposition and holomorphic Lefschetz formula, we calculate the Poincaré polynomials of the moduli spaces in low degrees.

Catanese, Fabrizio
Published in
Japanese Journal of Mathematics

Kodaira fibred surfaces are remarkable examples of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological characterization of Kodaira fibrations is emblematic of the use of topological methods in the study of moduli spaces of surfaces and higher dimensional c...

Karmazyn, Joseph
Published in
manuscripta mathematica

In the setting of a variety X admitting a tilting bundle T we consider the problem of constructing X as a quiver GIT quotient of the algebra A:=EndX(T)op\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddside...

Borghesi, Simone Tomassini, Giuseppe
Published in
Annali di Matematica Pura ed Applicata (1923 -)

In this article we give two notions of hyperbolicity for groupoids on the analytic site of complex spaces, which we call Kobayashi and Brody hyperbolicity. In the special case the groupoid is a complex analytic space, these notions of hyperbolicity give the classical ones due to Kobayashi and Brody. We prove that such notions are equivalent if the ...

Liu, Xiaolei
Published in
Chinese Annals of Mathematics, Series B

The modular invariants of a family of curves are the degrees of the pullback of the corresponding divisors by the moduli map. The singularity indices were introduced by Xiao (1991) to classify singular fibers of hyperelliptic fibrations and to compute global invariants locally. In semistable case, the author shows that the modular invariants corres...

Papadakis, Stavros Argyrios Van Steirteghem, Bart
Published in
Algebras and Representation Theory

We determine, under a certain assumption, the Alexeev–Brion moduli scheme M of affine spherical G-varieties with a prescribed weight monoid . In Papadakis and Van Steirteghem (Ann. Inst. Fourier (Grenoble). 62(5) 1765–1809 19) we showed that if G is a connected complex reductive group of type A and is the weight monoid of a spherical G-module, then...