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

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

2011-03-22

arxiv.org/abs/1103.4292v2

Bulletin of the LMS 2012 http://blms.oxfordjournals.org/cgi/content/abstract/bds043? ijkey=SznEjrf83QH1vdu&keytype=ref

Mathematics

Algebraic Geometry

Final version: main result generalized, title changed accordingly. To appear in Bulletin of the LMS

Scientific paper

10.1112/blms/bds043

Let S be a minimal complex surface of general type with irregularity q>=2 and let C be an irreducible curve of geometric genus g contained in S. Assume that C is "Albanese defective", i.e., 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 K^2_S and g for the canonical degree K_SC of C. As a corollary, we obtain a bound for the canonical degree of curves with g<= q-1, thereby generalizing and sharpening the main result of [S.Y. Lu, On surfaces of general type with maximal Albanese dimension, J. Reine Angew. Math. 641 (2010), 163-175].

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