A uniform bound on the canonical degree of Albanese defective curves on surfaces

Author： Lopes Margarida Mendes   Pardini Rita  

Publisher： Oxford University Press

ISSN： 0024-6093

Source： Bulletin of the London Mathematical Society, Vol.44, Iss.6, 2012-12, pp. : 1182-1188

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Abstract

Let S be a minimal complex surface of general type with irregularity q2 and let C S be an irreducible curve of geometric genus g. Assume that C is Albanese defective, that is, that the image of C via the Albanese map does not generate the Albanese variety Alb(S); we obtain a linear upper bound in terms of K2S and g for the canonical degree KSC of C. As a corollary, we obtain a bound for the canonical degree of curves with gq1, thereby generalizing and sharpening the main result of Lu [On surfaces of general type with maximal Albanese dimension, J. reine angew. Math. 641 (2010) 163175.].

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