1.1 Statement and Context. One of the underlying principles in the study of Kleinian groups is that aspects of the complex projective geometry of quotients of Ĉ by the groups reflect properties of the threedimensional hyperbolic geometry of the quotients of H by the groups. Yet, even though it has been over thirty-five years since Lipman Bers wrote down a holomorphic embedding of the Teichmülle...

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

For a Calabi–Yau 4-fold ( X , ω ) where is quasi-projective and nowhere vanishing section of its canonical bundle K the (derived) moduli stack compactly supported perfect complexes M −2-shifted symplectic thus has an orientation O → in sense Borisov–Joyce [11] necessary for defining Donaldson–Thomas type invariants . We extend first orientability result Cao–Gross–Joyce [23] to projective spin 4...

We compare various groups of 0-cycles on quasi-projective varieties over a field. As applications, we show that for certain singular projective varieties, the Levine-Weibel Chow group coincides with corresponding Friedlander-Voevodsky motivic cohomology. also an algebraically closed field positive characteristic, modulus smooth variety respect to reduced divisor Suslin homology complement divis...

Abstract We prove that if X is a regular quasi-projective variety of dimension d , the set line bundles {