Homotopy groups of the complements to singular hypersurfaces

L 2-Betti numbers of plane algebraic curves

“…In this sense this result is in the same vein as the results of Libgober [Lib82] and Cogolludo-Florens [CF07], but see also [Lib94,DM07,Ma06] for similar results in the higher-dimensional case. …”

Polynomials and Vanishing Cycles

“…Such a progress would not have been possible without the contribution of a long list of articles around the Lefschetz slicing principle, from which we took a part of the inspiration, such as [AF,Ch1,Ch2,Fu,FL,GM,HL1,HL2,HL3,La,Lef,Li,Lo,Mi]. Results of Zariski-van Kampen type have been proved by Libgober for generic Lefschetz pencils of hyperplanes and in the particular case when X is the complement in P n or C n of a hypersurface with isolated singularities [Li].…”

Higher-order Alexander invariants of plane algebraic curves

“…In Theorem 4.1, we find an upper bound in terms of the Milnor number of each singularity. In Theorem 4.5, we find an upper bound in terms of the Harvey's invariants,δ n , associated to each of the singular points of C. This result is analogous to the divisibility properties for the infinite cyclic Alexander polynomial of the complement (e.g., see [10], [11], [12], [17]). As a corollary to these theorems, we have that, if C is a curve in general position at infinity, then δ n (C) is finite, and therefore A n (C) is a torsion ZΓ n -module.…”

“…However, if the line at infinity is not transverse to the irreducible curve C, then the upper bounds mentioned above will also include the contribution of the singular points at infinity (similar to [11], Thm. 4.3).…”