Parametrizing maximal compact subvarieties
نویسندگان
چکیده
منابع مشابه
Subvarieties in non-compact hyperkähler manifolds
Let M be a hyperkähler manifold, not necessarily compact, and S ∼= CP 1 the set of complex structures induced by the quaternionic action. Trianalytic subvariety of M is a subvariety which is complex analytic with respect to all I ∈ CP . We show that for all I ∈ S outside of a countable set, all compact complex subvarieties Z ⊂ (M, I) are trianalytic. For M compact, this result was proven in [V1...
متن کاملParametrizing Shimura Subvarieties of A1 Shimura Varieties and Related Geometric Problems
This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of Xa,b = (H ) × (H). A special case describes all Shimura subvarieties of type A1 Shimura varieties. We produce, for any n ≥ 1, examples of manifolds/Shimura varieties with precisely n commensurability classes of totally geodesic submanifolds/Shimura sub...
متن کاملMaximal (sequentially) compact topologies
We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in which convergent sequences have unique limits. We also answer a question of D.E. Cameron by showing that each sequentially compact topology is contained in a ...
متن کاملMaximal Tori of Compact Lie Groups
A Lie group G is a real or complex differentiable manifold together with a group structure, where the group operations (multiplication and inverse) are differentiable. E.g., U(n) = {A ∈ GL(n,C) |A = A} is a real (and not complex!) Lie group. The tangent space TeG at the unit element e of G reflects the structure of the Lie group through the derivative of the so-called adjoint representation (no...
متن کاملThe Surface Parametrizing Cuboids
We study the surface S̄ parametrizing cuboids: it is defined by the equations relating the sides, face diagonals and long diagonal of a rectangular box. It is an open problem whether a ‘rational box’ exists, i.e., a rectangular box all of whose sides, face diagonals and long diagonal have (positive) rational length. The question is equivalent to the existence of nontrivial rational points on S̄. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1996
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-96-03153-x