Abstract
Given a minimal surface S equipped with a generically finite map to an Abelian variety and C ⊂ S a rational or an elliptic curve, we show that the canonical degree of C is bounded by four times the self-intersection of the canonical divisor of S. As a corollary, we obtain the finiteness of rational and elliptic curves with an optimal uniform bound on their canonical degrees on any surface of general type with two linearly independent regular one forms.
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Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
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