On a Conjecture on Linear Systems

2015/04/08 by Anand, Sonica
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.01905

Abstract

In a remark to Green's conjecture, Paranjape and Ramanan analyzed the vector bundle E which is the pullback by the canonical map of the universal quotient bundle T_\Pp^g-1(-1) on \Pp^g-1 and stated a more general conjecture and proved it for the curves with Clifford Index 1 (trigonal and plane quintic). In this paper, we state the conjecture for general linear systems and obtain the results for the case of hyperelliptic curves.

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• A local proof of Petri's conjecture at the general curve
• Green's Conjecture for the generic canonical curve
• A note on the linear systems on the projective bundles over Abelian varieties
• Moduli spaces of curves with linear series and the slope conjecture