IMAS   23417
INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Height of varieties in multiprojective spaces and arithmetic Nullstellens\"atze
Autor/es:
D'ANDREA, CARLOS; KRICK, TERESA; SOMBRA, MARTÍN
Lugar:
Tossa de Mar
Reunión:
Congreso; Heights 2011; 2011
Resumen:
We present bounds for the degree and the height of the polynomials arising in some central problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A~key role is played by the notion of {canonical mixed heights} of multiprojective varieties. We study this notion from the point of view of resultant theory and establish some of its basic properties, including its behavior with respect to intersections, projections and products. We obtain analogous results for the function field case, including a parametric Nullstellensatz.