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Javier Fernandez de Bobadilla

Group Leader. Ikerbasque Research Professor

Singularity Theory and Algebraic Geometry

T +34 946 567 842
F +34 946 567 842
E jbobadilla@bcamath.org

Information of interest

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.
 

  • COHOMOLOGY OF CONTACT LOCI 

    Budur, N.Autoridad BCAM; Fernández de Bobadilla, J.Autoridad BCAM; Le, Q.; Nguyen, D. (2022-01-01)
    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 of a log resolution and coincides with ...

  • Moderately Discontinuous Homology 

    Fernández de Bobadilla, J.Autoridad BCAM; Heinze, S.; Sampaio, J.E.; Pe Pereira, M. (2021-01-01)
    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 

    Fernández de Bobadilla, J.Autoridad BCAM; Pe Pereira, M. (2020-03-01)
    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 

    Fernández de Bobadilla, J.Autoridad BCAM; Nuño-Ballesteros, J.J.; Peñafort Sanchis, Guillermo (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 

    Fernandes, A.; Fernández de Bobadilla, J.Autoridad BCAM; Sampaio, J.E. (2018-08-29)
    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 ...

  • The Nash Problem from a Geometric and Topological Perspective 

    Fernández de Bobadilla, J.Autoridad BCAM; Pe Pereira, M. (2018-04-17)
    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- ...

  • Representation of surface homeomorphisms by tête-à-tête graphs 

    Fernández de Bobadilla, J.Autoridad BCAM; Pe Pereira, M.; Portilla Cuadrado, P. (2017-06-21)
    We use tête-à-tête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with non-empty boundary, improving work of N. A'Campo and C. Graf. We also introduce ...

  • Equisingularity in One-Parameter Families of Generically Reduced Curves 

    Fernández de Bobadilla, J.Autoridad BCAM; Snoussi, J.; Spivakovsky, M. (2016-01-01)
    We explore some equisingularity criteria in one-parameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski’s discriminant criterion. We prove that topological triviality ...

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