Covering Relations between Ball-quotient Orbifolds
نویسنده
چکیده
Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinitely many orbifolds on P uniformized by the complex 2-ball B2 and some orbifolds over K3 surfaces uniformized by B2. We also give, along with infinitely many reducible examples, an infinite series of irreducible curves along which P is uniformized by the product of 1-balls B1× B1.
منابع مشابه
Forgetful Maps between Deligne-mostow Ball Quotients
We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livné fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimension...
متن کاملScalar-flat Kähler Orbifolds via Quaternionic-complex Reduction
We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k − 1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group c...
متن کاملQuotient Stacks and String Orbifolds
In this short review we outline some recent developments in understanding string orbifolds. In particular, we outline the recent observation that string orbifolds do not precisely describe string propagation on quotient spaces, but rather are literally sigma models on objects called quotient stacks, which are closely related to (but not quite the same as) quotient spaces. We show how this is an...
متن کاملString Orbifolds and Quotient Stacks
In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling definitions, and is further justified by a number of results. Quotient stacks are very closely related to quotient spaces; for example, when the orbifold group ac...
متن کاملIntroduction to Orbifolds
Orbifolds lie at the intersection of many different areas of mathematics, including algebraic and differential geometry, topology, algebra and string theory. Orbifolds were first introduced into topology and differential geometry by Satake [6], who called them V-manifolds. Satake described them as topological spaces generalizing smooth manifolds and generalized concepts such as de Rham cohomolo...
متن کامل