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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 .

On ranks of Jacobian varieties in prime degree extensions

Dave Mendes da Costa (2013)

Acta Arithmetica

T. Dokchitser [Acta Arith. 126 (2007)] showed that given an elliptic curve E defined over a number field K then there are infinitely many degree 3 extensions L/K for which the rank of E(L) is larger than E(K). In the present paper we show that the same is true if we replace 3 by any prime number. This result follows from a more general result establishing a similar property for the Jacobian varieties associated with curves defined by an equation of the shape f(y) = g(x) where f and g are polynomials...

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