相关论文: Rigid geometry on projective varieties

We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety…

For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.

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 note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.

In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.

In this paper we studied a broader type of generalized balls which are domains on the complex projective with possibly Levi-degenerate boundaries. We proved rigidity theorems for proper holomorphic mappings among them by exploring the…

In this note, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to $\mathcal{C}^2$-smooth maps on the boundary.

We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.

An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.

In this survey paper, we outline the proofs of the rigidity results for simple, thick, hyperbolic P-manifolds found in our three earlier papers math.GR/0506518, math.GT/0410476, and math.GR/0409586. We discuss how the arguments change in…

We study the local rigidity of projective smooth horospherical varieties of rank one and Picard number two. These varieties have been already considered by the second author in a work where their automorphism groups are computed. The…

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

A classical result in complex geometry says that the automorphism group of a manifold of general type is discrete. It is more generally true that there are only finitely many surjective morphisms between two fixed projective manifolds of…

Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.

In this paper, we establish an innovative framework in logarithmic Hodge theory for toroidal varieties, introducing weighted toroidal structures and developing a systematic obstruction theory for Hodge classes. Building upon recent advances…

In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.

We prove rigidity facts for groups acting on pseudo-Riemannian manifolds by preserving unparameterized geodesics.

In this article, we prove a rigidity criterion for period maps of admissible variations of graded-polarizable mixed Hodge structure, and establish rigidity in a number of cases, including families of quasi-projective curves, projective…

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 give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.