Related papers: A closer look at semistability for singular princi…

Let K be a discretly henselian field whose residue field is separably closed. Answering a question raised by G. Prasad, we show that a semisimple K-- group G is quasi-split if and only if it quasi--splits after a finite tamely ramified…

Let $G$ be a connected reductive affine algebraic group defined over $\mathbb C$, and let $\Gamma$ be a cocompact lattice in $G$. We prove that any invariant bundle on $G/\Gamma$ is semistable.

We set up some basic module theory over semirings, with particular attention to what is needed in scheme theory over semirings. We show that while not all the usual definitions of vector bundle agree over semirings, all the usual…

We prove that the affine closure of the cotangent bundle of the basic affine space of a complex semisimple group has conical symplectic singularities, which confirms a conjecture of Ginzburg and Kazhdan. We also show that this variety is…

Let $X$ be a complex projective manifold. Fix two ample line bundles $H_0$ and $H_1$ on $X$. It is the aim of this note to study the variation of the moduli spaces of Gieseker semistable sheaves for polarizations lying in the cone spanned…

Let $X$ be a smooth irreducible projective curve. Recently, Pauly and Pe\'on-Nieto shows that a vector bundle over $X$ is very stable if and only if the Hitchin map on the vector space of Higgs field on that vector bundle is proper. In this…

We define functorial isomorphisms of parallel transport along \'etale paths for a class of principal $G$-bundles on a $p$-adic curve. Here $G$ is a connected reductive algebraic group of finite presentation and the considered principal…

Let M be a complex projective manifold with the property that for any compact Riemann surface C and holomorphic map f: C -> M the pullback of the tangent bundle of M is semistable. We prove that in this case M is a curve or a finite etale…

Let $X$ be a compact connected Riemann surface of genus at least two, and let ${G}$ be a connected semisimple affine algebraic group defined over $\mathbb C$. For any $\delta \in \pi_1({G})$, we prove that the moduli space of semistable…

We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular,…

Let $G$ be an arbitrary (not necessarily isomorphic to a closed subgroup of $\mathrm{GL}(r,\mathbb{C})$) complex Lie group, $U$ a complex manifold and $p:P\to U$ a $\mathcal{C}^\infty$ principal $G$-bundle on $U$. We introduce and study the…

We describe the primitive central idempotents of the group algebra over a number field of finite monomial groups. We give also a description of the Wedderburn decomposition of the group algebra over a number field for finite strongly…

Let $G$ be a semisimple algebraic group defined over an algebraically closed field of characteristic 0 and $P$ be a parabolic subgroup of $G$. Let $M$ be a $P$-module and $V$ be a $P$-stable closed subvariety of $M$. We show in this paper…

By virtue of the well-known theorem, a structure Lie group G of a principal bundle P is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/H. In gauge theory, such sections are treated as classical…

Let X be a smooth complex projective curve of genus g bigger or equal to 1. If g is bigger than 1 assume further that X is either bielliptic or with general moduli. Under a natural condition on slopes, we prove that there exists a short…

We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…

After recalling the basic notions concerning Higgs-Grassmannian schemes, I review how these latter can be used to define generalisations of the notion of positivity conditions, such as numerically flatness, which "feel" the Higgs field.…

We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we…

Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…

Let $E_G$ be a stable principal $G$--bundle over a compact connected Kaehler manifold, where $G$ is a connected reductive linear algebraic group defined over the complex numbers. Let $H\subset G$ be a complex reductive subgroup which is not…