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On proximity relations for valuations dominating a two-dimensional regular local ring.

José J. Aparicio, Angel Granja, Tomás Sánchez-Giralda (1999)

Revista Matemática Iberoamericana

The purpose of this paper is to define a new numerical invariant of valuations centered in a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers δν = {δν(j)}j ≥ 0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν. This sequence is characterized by seven combinatorial properties, so that any sequence of non-negative rational numbers having the above properties...

On rank 2 semistable vector bundles over an irreducible nodal curve of genus 2

Sonia Brivio (1998)

Bollettino dell'Unione Matematica Italiana

Sia C una curva irriducibile nodale di genere aritmetico p a = 2 . In queste note vogliamo mostrare come il sistema lineare delle quadriche, contenenti un opportuno modello proiettivo della curva, permette di descrivere i fibrati vettoriali semistabili, di rango 2 , su C .

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