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...

Li, Ling Guang
Published in
Acta Mathematica Sinica, English Series

Let k be an algebraically closed field of characteristic p > 0, X a smooth projective variety over k with a fixed ample divisor H, FX : X → X the absolute Frobenius morphism on X. Let E be a rational GLn(k)-bundle on X, and ρ : GLn(k) → GLm(k) a rational GLn(k)-representation of degree at most d such that ρ maps the radical RGLn(k)) of GLn(k) into ...

Isaev, Alexander
Published in
The Journal of Geometric Analysis

Let d≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\ge 3$$\end{document}, n≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{am...

Kapovich, M Kumar, S Millson, JJ

We explicitly calculate the triangle inequalities for the group PSO(8). Therefore we explicitly solve the eigenvalues of sum problem for this group (equivalently describing the side-lengths of geodesic triangles in the corresponding symmetric space for the Weyl chamber-valued metric). We then apply some computer programs to verify two basic questio...

Gallardo, Patricio Martinez-Garcia, Jesus Zhang, Zheng
Published in
European Journal of Mathematics

We study the moduli space of triples (C,L1,L2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(C, L_1, L_2)$$\end{document} consisting of quartic curves C and lines L1\...

Pelletier, Maxime
Published in
manuscripta mathematica

We give another proof, using tools from Geometric Invariant Theory, of a result due to Sam and Snowden in (J Algebraic Comb 43(1):1–10, 2016), concerning the stability of Kronecker coefficients. This result states that some sequences of Kronecker coefficients eventually stabilise, and our method gives a nice geometric bound from which the stabilisa...

Fujita, Kento
Published in
Mathematische Annalen

Assume that a projective variety together with a polarization is uniformly K-stable. If the polarization is canonical or anti-canonical, then the projective variety is uniformly K-stable with respects to any polarization sufficiently close to the original polarization.

Schmitt, Johannes
Published in
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

For a complex variety X^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{X}$$\end{document} with an action of a reductive group G^\documentclass[12pt]{minimal} ...

Gallardo, Patricio Routis, Evangelos
Published in
European Journal of Mathematics

We introduce and study smooth compactifications of the moduli space of n labeled points with weights in projective space, which have normal crossings boundary and are defined as GIT quotients of the weighted Fulton–MacPherson compactification. We show that the GIT quotient of a wonderful compactification is also a wonderful compactification under c...

Biliotti, Leonardo Zedda, Michela
Published in
Annali di Matematica Pura ed Applicata (1923 -)

We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of noncompact real reductive Lie groups on topological spaces that admit functions similar to the Kempf–Ness function. The point of this construction is that one can c...