Related papers: On Rigidity and the Albanese Variety for Paralleli…

To each complex composition algebra $\mathbb{A}$, there associates a projective symmetric manifold $X(\mathbb{A})$ of Picard number one, which is just a smooth hyperplane section of the following varieties ${\rm Lag}(3,6), {\rm Gr}(3,6),…

In this paper we prove the following rigidity theorem: a generic analytic polyhedron with non-compact automorphism group is biholomorphic to the product of a complex manifold with compact automorphism group and a polydisk. Moreover, this…

To every Fell bundle $\mathscr C$ over a locally compact group ${\sf G}$ one associates a Banach $^*$-algebra $L^1({\sf G}\,\vert\,\mathscr C)$. We prove that it is symmetric whenever ${\sf G}$ with the discrete topology is rigidly…

A topological commutative ring is said to be rigid when for every set $X$, the topological dual of the $X$-fold topological product of the ring is isomorphic to the free module over $X$. Examples are fields with a ring topology, discrete…

By Hantzsche-Wendt manifold (for short HW-manifold) we understand any oriented closed Riemannian manifold of dimension n with a holonomy group (Z_2)^{n-1}. Two HW-manifolds M_1 and M_2 are cohomological rigid if and only if a homeomorphism…

For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are…

A compact complex manifold X is said to be rationally cohomologically rigidified if its automorphism group Aut(X) acts faithfully on the cohomology ring H*(X,Q). In this note, we prove that, surfaces of general type with irregularity q>2…

In the study of holomorphic maps, the term "rigidity" refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this…

Let $X$ be a noncommutative real compact algebraic manifold, in the sense that $C(X)=C^*(x_1,\ldots,x_N|x_i=x_i^*,f_\alpha(x_1,\ldots,x_N)=0)$, with $f_\alpha\in\mathbb R<x_1,\ldots,x_N>$. Associated to $X$ are its classical version…

A rigid cohomology class on a complex manifold is a class that is represented by a unique closed positive current. The positive current representing a rigid class is also called rigid. For a compact Kahler manifold $X$ all eigenvectors of…

We classify smooth Schubert varieties S_0 in a rational homogeneous manifold S associated to a short root, and show that they are rigid in the sense that any subvariety of S having the same homology class as S_0 is induced by the action of…

In this short note we prove that if X is a separably rationally connected variety over an algebraically closed field of positive characteristic, then H^1(X, O_X)=0.

Let X be a normal quasi-projective variety over $\mathbb{C}$. We study its higher Albanese manifolds, introduced by Hain and Zucker, from the point of view of o-minimal geometry. We show that for each $s$ the higher Albanese manifold…

We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.

In this paper, we prove some rigidity theorems for compact Bach-flat $n$-manifold with the positive constant scalar curvature. In particular, our conditions in Theorem 1.4 have the additional properties of being sharp.

We show that under mild set theoretic hypotheses we have rigidity for algebras of continuous functions over Higson coronas, topological spaces arising in coarse geometry. In particular, we show that under $\mathsf{OCA}$ and $\mathsf…

In this paper we study the variability and rigidity of secondary characteristic classes which arise from flat connections on a manifold. Considering the connection as a Lie-algebra valued one-form, we study the characteristic map from Lie…

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube…

We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theorems for the relevant Picard varieties, together with recent…

In this paper, we study the rigidity properties of compact Kahler manifolds. Given a smooth family of compact Kahler manifolds X over the unit disk, we show that all the fibers are mutually isomorphic if the family is locally trivial at a…