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arXiv · 2305.17923

A remark on the canonical degree of curves on smooth projective surface

Ciro Ciliberto·Claudio Fontanari
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Abstract

The canonical degree $C.K_X$ of an integral curve on a smooth projective surface $X$ is conjecturally bounded from above by an expression of the form $A(g-1)+B$, where $g$ is the geometric genus of $C$ and $A$, $B$ are constants depending only on $X$. We prove that this conjecture holds with $A = -1$ under the assumptions $h^0(X, -K_X) = 0$ and $h^0(X, 2K_X + C) = 0$.

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Ciro Ciliberto, Claudio Fontanari. 2023-05-29. A remark on the canonical degree of curves on smooth projective surface. https://arxiv.org/abs/2305.17923

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