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arXiv · 2205.13318

On the slope inequalities for extremal curves

Valentina Beorchia·Michela Brundu
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Abstract

The present paper concerns the question of the violation of the r-th inequality for extremal curves in the projective r-space, posed by T. Kato and G. Martens. We show that the answer is negative in many cases. The result is obtained by a detailed analysis of the geometry of extremal curves and their canonical model. As a consequence, we show that particular curves on a Hirzebruch surface do not violate the slope inequalities in a certain range.

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Valentina Beorchia, Michela Brundu. 2022-05-26. On the slope inequalities for extremal curves. https://arxiv.org/abs/2205.13318

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