We construct examples to show that having nef cotangent bundle is not preserved under finite ramified covers. Our also a projective manifold with Stein universal cover may have bundle, disproving conjecture of Liu–Maxim–Wang [7].

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

We reduce certain proofs in [16, 11, 12] to depth two quasibases from one side only, a minimalistic approach which leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property. We prove that a proper algebra extension is a left T -Galois extension for some right finite projective left bialgebroid over some algebra R if and only if ...

In this note we reduce certain proofs in [9, 5, 6] to depth two quasibases from one side only. This minimalistic approach leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property: a proper algebra extension is a left T -Galois extension for some right finite projective left bialgebroid T over some algebra R if and only if it is...

We consider a central division algebra (over a field) endowed with a quadratic pair or with a symplectic involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. This covers a recent conjecture raised by M. Zhykhovich. The remaining related projective homogeneous varieties are 2-compressible in general. Let F be a field, n ≥ 1, D a central division...

We describe some of the connections between the Bieri–Neumann– Strebel–Renz invariants, the Dwyer–Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties of regular, free abelian covers of X can be expressed in terms of the resonance varieties, extracted from the cohomology ring of X. In general, though, tran...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

We define a restricted class of non-projective trees that 1) covers many natural language sentences; and 2) can be parsed exactly with a generalization of the popular arc-eager system for projective trees (Nivre, 2003). Crucially, this generalization only adds constant overhead in run-time and space keeping the parser’s total run-time linear in the worst case. In empirical experiments, our prop...