The present paper concerns the question of the violation of the r-th inequality for extremal curves in Pr , posed in [KM]. We show that the answer is negative in many cases (Theorem 4.13 and Corollary 4.14). 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 (Theorem 6.4).

On the slope inequalities for extremal curves

Beorchia, Valentina
Membro del Collaboration Group
;
Brundu, Michela
Membro del Collaboration Group
2022-01-01

Abstract

The present paper concerns the question of the violation of the r-th inequality for extremal curves in Pr , posed in [KM]. We show that the answer is negative in many cases (Theorem 4.13 and Corollary 4.14). 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 (Theorem 6.4).
2022
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https://link.springer.com/article/10.1007/s13366-022-00662-y
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3029939
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