Related papers: Modifications of the Levi core

L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of a locally symmetric space. We define the micro-support of an L-module; it is a set of irreducible modules for the Levi…

We prove that the lattice of normal subgroups of ultraproducts of compact simple non-abelian groups is distributive. In the case of ultraproducts of finite simple groups or compact connected simple Lie groups of bounded rank the set of…

A locally conformally product (LCP) structure on a compact conformal manifold is a closed non-exact Weyl connection (i.e.~a linear connection which is locally but not globally the Levi-Civita connection of Riemannian metrics in the…

For a finite-dimensional Lie algebra $\mathfrak{L}$ over $\mathbb{C}$ with a fixed Levi decomposition $\mathfrak{L} = \mathfrak{g} \oplus \mathfrak{r}$ where $\mathfrak{g}$ is semi-simple, we investigate $\mathfrak{L}$-modules which…

Let $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ be a Levi decomposable Lie algebra, with Levi factor $\mathfrak{s}$, and radical $\mathfrak{r}$. A module $V$ of $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ is cyclic indecomposable if it is…

We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform along their Hodge locus in the universal locally trivial…

Let $C$ be a comb-like curve over $\mathbb{C}$, and $E$ be a vector bundle of rank $n$ on $C$. In this paper, we investigate the criteria for the semistability of the restriction of $E$ onto the components of $C$ when $E$ is given to be…

We consider the space $\mathcal{D}'^r_L(M;E)$ of distributional sections of the smooth complex vector bundle $E\rightarrow M$ whose Sobolev wave front set of order $r\in\mathbb{R}$ lies in the closed conic subset $L$ of $T^*M\backslash0$.…

Let $|L|$ be a linear system on a smooth complex Enriques surface $S$ whose general member is a smooth and irreducible curve of genus $p$, with $L^ 2>0$, and let $V_{|L|, \delta} (S)$ be the Severi variety of irreducible $\delta$-nodal…

Modifications of bundles over complex curves is an operation that allows one to construct a new bundle from a given one. Modifications can change a topological type of bundle. We describe the topological type in terms of the characteristic…

Let $M$ be an irreducible projective variety over an algebraically closed field $k$ of characteristic zero equipped with an action of a group $\Gamma$. Let $E_G$ be a principal $G$--bundle over $M$, where $G$ is a connected reductive…

The purpose of this note is to give a simple proof of the fact that a certain substack, defined in [2], of the moduli stack $T^{\ast}Bun_G(\Sigma)$ of Higgs bundles over a curve $\Sigma$, for a connected, simply connected semisimple group…

We prove that all SYM theories that have a quantum modified moduli space $\m$ defined by a single constraint equation have trivial homotopy groups $\pi_j(\m)$ for $j=0,1,2,3$ and 4. This implies that none of these theories admit skyrmions…

Given a quadratic CR manifold $\mathcal{M}$ embedded in a complex space, and a holomorphic function $f$ on a tubular neighbourhood of $\mathcal{M}$, we show that the $L^p$-norms of the restriction of $f$ to the translates of $\mathcal{M}$…

We introduce the notion of basic slc-trivial fibrations. It is a generalization of that of Ambro's lc-trivial fibrations. Then we study fundamental properties of basic slc-trivial fibrations by using the theory of variations of mixed Hodge…

Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate…

Let $G\subset\GL(V)$ be a complex reductive group where $\dim V<\infty$, and let $\pi\colon V\to\quot VG$ be the categorical quotient. Let $\NN:=\pi\inv\pi(0)$ be the null cone of $V$, let $H_0$ be the subgroup of $\GL(V)$ which preserves…

Let $E$ be a vector bundle on a smooth complex projective variety $X$. We study the family of sections $s_t\in H^0(E\otimes L_t)$ where $L_t\in Pic^0(X)$ is a family of topologically trivial line bundle and $L_0=\mathcal O_X,$ that is, we…

We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…

This paper present homogeneous CR hypersurfaces satisfying the $CR$-invariant property of being $k$-nondegenerate for an arbitrary integer $k\geq 1$. The construction of such homogeneous manifolds are based on $CR$ algebras defined by…