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Edoardo Ballico

  1. Complexity of multivariate polynomial evaluation.

    Wed, 06/15/2011 - 15:01 — SomNambul
    Authors: Edoardo Ballico, Massimiliano Sala, Michele Elia
    Subjects: Commutative Algebra
    Abstract

    We describe a method to evaluate multivariate polynomials over a finite field
    and discuss its multiplicative complexity.

  2. Meromorphic Line Bundles and Holomorphic Gerbes.

    Thu, 01/13/2011 - 16:01 — SomNambul
    Authors: Edoardo Ballico, Oren Ben-Bassat
    Subjects: Algebraic Geometry
    Abstract

    We show that any complex manifold that has a divisor whose normalization has
    non-zero first Betti number either has a non-trivial holomorphic gerbe which
    does not trivialize meromorphicly or a meromorphic line bundle not equivalent
    to any holomorphic line bundle. Similarly, higher Betti numbers of divisors
    correspond to higher gerbes or meromorphic gerbes. We give several new
    examples.

  3. On the X-rank with respect to linear projections of projective varieties.

    Fri, 12/25/2009 - 16:01 — SomNambul
    Authors: Edoardo Ballico, Alessandra Bernardi
    Subjects: Algebraic Geometry
    Abstract

    In this paper we improve the known bound for the $X$-rank $R_{X}(P)$ of an
    element $P\in {\mathbb{P}}^N$ in the case in which $X\subset {\mathbb P}^n$ is
    a projective variety obtained as a linear projection from a general
    $v$-dimensional subspace $V\subset {\mathbb P}^{n+v}$.

  4. Koszul cohomology and singular curves.

    Thu, 09/17/2009 - 10:33 — SomNambul
    Authors: Claudio Fontanari, Edoardo Ballico, Luca Tasin
    Subjects: Algebraic Geometry
    Abstract

    We investigate Koszul cohomology on irreducible nodal curves. In particular,
    we prove both Green and Green-Lazarsfeld conjectures for the general k-gonal
    nodal curve.

  5. Smoothing of rational m-ropes.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: Edoardo Ballico, Elizabeth Gasparim, Thomas Köppe
    Subjects: Algebraic Geometry
    Abstract

    In a recent paper, Gallego, Gonz\'{a}lez and Purnaprajna showed that rational
    3-ropes can be smoothed. We generalise their proof and obtain smoothability of
    rational $m$-ropes for $m \geq 3$.

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