[Todos CMAT] Nueva actividad del Workshop: Charla de Teresa Krick

Diego Armentano diego en cmat.edu.uy
Mar Abr 12 12:20:59 UYT 2011

Hola a todos.
Esta tarde a las 16:00hs Teresa Krick va  a dar una charla en el marco del
Workshop en Complejidad, el cual se esta desarrollando en el piso 14 del


   *On arithmetic effective Nullstellensätze and **implicitization problems*


Joint work  with Carlos D'Andrea and Martin Sombra, on precise bounds for
the effective Nullstellensatz and the implicitation problem  in their
arithmetic aspects.

The Nullstellensatz establishes that if f_1,...,f_s in k[x_1,...,x_n] are
polynomials with no common roots in the algebraic closure of the field k,
then they satisfy a Bezout identity 1=g_1f_1+...+g_sf_s for some polynomials
g_1,...,g_s in k[x_1,...,x_n].

The implicitization problem consists in computing equations for an
algebraic variety from a given rational parameterization of it. The typical
case is when the variey is a hypersurface, in which case it is defined by a
single ``implicit equation'' and the problem
consists in computing  it.

I will discuss degree and height bounds for these problems for the cases
when the polynomials are defined over the rational numbers or over a field
of rational functions, which we obtain by studying
heights of varieties in multiprojective spaces.

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