We construct a multiplicative spectral sequence converging to the symplectic cohomology
ring of any affine variety X, with first page built out of topological invariants associated to …

We show that every family of isolated hypersurface singularities with constant Milnor number
has constant multiplicity. To achieve this, we endow the A'Campo model of “radius zero” …

The main approach to study algebraic singularities is to introduce invariants that allow us to
measure how singular a point in an algebraic variety is. Once the invariant is introduced, the …

We construct a spectral sequence converging to the cohomology with compact support of
the m-th contact locus of a complex polynomial. The first page is explicitly described in terms …

Let k be a field of characteristic zero and let X be an algebraic k-variety endowed with an
action of the multiplicative algebraic monoid A 1. In this article, we prove that the nearby …

The embedded Nash problem for a hypersurface in a smooth algebraic variety, is to
characterize geometrically the maximal irreducible families of arcs with fixed order of contact …

We show that every family of isolated hypersurface singularities with constant Milnor number
has constant multiplicity. To achieve this, we endow the A'Campo model of" radius zero" …

arXiv:2408.01533v1 [math.AG] 2 Aug 2024 Page 1 arXiv:2408.01533v1 [math.AG] 2 Aug 2024
THE EMBEDDED NASH PROBLEM ON SINGULAR SPACES: THE CASE OF SURFACES …

The variation operator in singularity theory maps relative homology cycles to compact cycles
in the Milnor fiber using the monodromy. We construct its symplectic analogue for an …

We give a new proof of Zariski's multiplicity conjecture in the case of isolated hypersurface
singularities; this was first proved by de Bobadilla-Pe\l ka\cite {BobadillaPelka}. Our proof …