Related papers: Antiholomorphic involutions and spherical subgroup…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
Let X be a holomorphically separable irreducible reduced complex space, K a connected compact Lie group acting on X by holomorphic transformations, theta : K -> K a Weyl involution, and mu : X -> X an antiholomorphic involution map…
Our purpose in this article is to study anti-invariant statistical submersions from holomorphic statistical manifolds. Firstly we introduce holomorphic statistical submersions satisfying the certain condition, after we give anti-invariant…
We study anti-holomorphic involutions of the moduli space of principal $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a complex semisimple Lie group. These involutions are defined by fixing anti-holomorphic involutions…
We classify involutions acting on spherical 3-manifolds up to conjugacy. Our geometric approach provides insights into numerous topological properties of these involutions.
We introduce an algebraic method for describing the Hodge filtration of degenerating hypersurfaces in projective toric varieties. For this purpose, we show some fundamental properties of logarithmic differential forms on proper equivariant…
This is a survey article on moduli of affine schemes equipped with an action of a reductive group. The emphasis is on examples and applications to the classification of spherical varieties.
We study the homogeneous involutions on the full square matrices over an algebraically closed field endowed with a division grading with commutative support. We obtain the classification of the isomorphism and equivalence classes for the…
It is proved that a Stein manifold acted on by a connected compact Lie group is spherical if and only if there exists an antiholomorphic involution preserving each orbit of the action. This involution can be chosen equivariant with respect…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
We initiate the study of analogues of symmetric spaces for the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions of the automorphism group, and determine…
We establish analytic linearization of s-proper analytic groupoids around invariant submanifolds. We apply this result to show that any such groupoid admits a holomorphic extension.
Conformal invariants of manifolds of non-positive scalar curvature are studied in association with growth in volume and fundamental group.
We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also…
We consider evolution equations for curves in the 3-dimensional sphere $S^3$ that are invariant under the group $SU(2,1)$ of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…
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.
We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of $\mathbb{T}^2$ in the homotopy class of any linear expanding map with integer eigenvalues. These examples exhibit branching of centre curves along…
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.