Oka properties of some hypersurface complements

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Multivariable Alexander Invariants of Hypersurface Complements

We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin’s vanishing theorem for perverse sheaves. We conclude with explicit computations of twisted cohomology following an idea already exploited in the hyperplane arrangement case, which combines the degen...

L–betti Numbers of Hypersurface Complements

In [DJL07] it was shown that if A is an affine hyperplane arrangement in Cn, then at most one of the L2–Betti numbers b i (C n \ A, id) is non–zero. In this note we prove an analogous statement for complements of complex affine hypersurfaces in general position at infinity. Furthermore, we recast and extend to this higher-dimensional setting results of [FLM09, LM06] about L2–Betti numbers of pl...

On the Alexander invariants of hypersurface complements

Massey Products of Complex Hypersurface Complements

The study of the topology of hypersurface complements is a classical subject in algebraic geometry. Most of what is known about these spaces is related to invariants of their rational homotopy type. In this paper, we attempt to show that their Fp-homotopy type captures in general more information than the Q-homotopy type, where Fp is the prime field of p elements. Let X be the complement to a h...