On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds.
Seiberg-Witten invariants and surface singularities.
The real Seifert form and the spectral pairs of isolated hypersurface singularities
Generalized local and global Sebastiani-Thom type theorems
The Milnor fiber and the zeta function of the singularities of type
Variation structures: results and open problems
The Seiberg–Witten invariants of negative definite plumbed 3-manifolds
Assume that is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of . The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph , and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second...
On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles
Let be a normal crossing divisor in the smooth complex projective algebraic variety and let be a tubular neighbourhood of in . Using geometrical properties of different intersections of the irreducible components of , and of the embedding , we provide the “normal forms” of a set of geometrical cycles which generate , where is one of the following pairs , , , and . The construction is compatible with the weights in of Deligne’s mixed Hodge structure. The main technical part...
Hodge–type structures as link invariants
Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge–type numerical invariants of any, not necessarily algebraic, link in a three–sphere. We call them
The geometric genus of hypersurface singularities
Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all superisolated and Newton non-degenerate hypersurface singularities.
On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance
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