Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to ...

Abstract. Let (X, o) be a complex normal surface singularity. We fix one of its good resolutions X → X, an effective cycle Z supported on the reduced exceptional curve, and any possible (first Chern) class l′ ∈ H 2 (X , ...

Abstract. In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over an essential line arrangement ...

For d ≥ 4, the Noether-Lefschetz locus NLd parametrizes smooth, degree d sur- faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the ...

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure ...

Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$-module $M(g)$ with the property that $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ...

Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and ...

We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz ...

A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbing 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function ...

In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ...