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+34 946 567 842
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+34 946 567 842
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jbobadilla@bcamath.org
Information of interest
 Orcid: 0000000237283986
I work in Singularity Theory and Algebraic Geometry. I am interested in singular spaces and maps. I have worked in arc spaces, normal surface singularities, geometry of degenerating families, intersection cohomology, Hodge theory and related techniques, Lipschitz geometry, characteristic classes of singular spaces, invariants coming from symplectic topology and in other aspects of geometry and topology of algebraic varieties.

Moderately discontinuous homotopy
(202212)

COHOMOLOGY OF CONTACT LOCI
(20220101)We construct a spectral sequence converging to the cohomology with compact support of the mth contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with ...

Moderately Discontinuous Homology
(20210101)We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow ...

The Nash Problem from Geometric and Topological Perspective
(20200301)We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional ...

A jacobian module for disentanglements and applications to Mond's conjecture
(2019)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)$, ...

Multiplicity and degree as bi‐Lipschitz invariants for complex sets
(20180829)We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer biLipschitz transformations (outer biLipschitz homeomorphims of germs in the first case and outer biLipschitz ...

The Nash Problem from a Geometric and Topological Perspective
(20180417)We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the au thors influenced it. Later we summarize the main ideas in the higher dimen ...

On the generalized Nash problem for smooth germs and adjacencies of curve singularities
(20171210)In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space ...

Representation of surface homeomorphisms by têteàtête graphs
(20170621)We use têteàtête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with nonempty boundary, improving work of N. A'Campo and C. Graf. We also introduce ...

Equisingularity in OneParameter Families of Generically Reduced Curves
(20160101)We explore some equisingularity criteria in oneparameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski’s discriminant criterion. We prove that topological triviality ...