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Alexandru Dimca

  1. Arithmetic group symmetry and finiteness properties of Torelli groups.

    Чт, 02/04/2010 - 16:01 — SomNambul
    Authors: Alexandru Dimca, Stefan Papadima
    Subjects: Group Theory
    Abstract

    We examine groups whose resonance varieties, characteristic varieties and
    Sigma-invariants have a natural arithmetic group symmetry, and we explore
    implications on various finiteness properties of subgroups. We compute
    resonance varieties, characteristic varieties and Alexander polynomials of
    Torelli groups, and we show that all subgroups containing the Johnson kernel
    have finite first Betti number, when the genus is at least four.

  2. Quasi-K\"ahler groups, 3-manifold groups, and formality.

    Чт, 01/07/2010 - 16:01 — SomNambul
    Authors: Alexandru Dimca, Alexander I. Suciu, Stefan Papadima
    Subjects: Algebraic Geometry
    Abstract

    In this note, we address the following question: Which 1-formal groups occur
    as fundamental groups of both quasi-K\"ahler manifolds and closed, connected,
    orientable 3-manifolds. We classify all such groups, at the level of Malcev
    completions, and compute their coranks. Dropping the assumption on
    realizability by 3-manifolds, we show that the corank equals the isotropy index
    of the cup-product map in degree one. Finally, we examine the formality
    properties of smooth affine surfaces and quasi-homogeneous isolated surface
    singularities.

  3. First Milnor cohomology of hyperplane arrangements.

    Пт, 08/21/2009 - 19:51 — SomNambul
    Authors: Nero Budur, Alexandru Dimca, Morihiko Saito
    Subjects: Algebraic Geometry
    Abstract

    We show a combinatorial formula for a lower bound of the dimension of the
    non-unipotent monodromy part of the first Milnor cohomology of a hyperplane
    arrangement satisfying some combinatorial conditions. This gives exactly its
    dimension if a stronger combinatorial condition is satisfied. We also prove a
    non-combinatorial formula for the dimension of the non-unipotent part of the
    first Milnor cohomology, which apparently depends on the position of the
    singular points. The latter generalizes a formula previously obtained by the
    second named author.

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