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- W2949366956 abstract "The emph{canonical degree} of a curve $C$ on a surface $X$ is $K_Xcdot C$. Our main result, is that on a surface of general type there are only finitely many curves with negative self--intersection and sufficiently large canonical degree. Our proof strongly relies on results by Miyaoka. We extend our result both to surfaces not of general type and to non--negative curves, and give applications, e.g. to finiteness of negative curves on a general blow--up of $mathbb P^ 2$ at $ngeq 10$ general points (a result related to emph{Nagata's Conjecture}). We finally discuss a conjecture by Vojta concerning the asymptotic behaviour of the ratio between the canonical degree and the geometric genus of a curve varying on a surface. The results in this paper go in the direction of understanding the emph{bounded negativity} problem." @default.
- W2949366956 created "2019-06-27" @default.
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- W2949366956 date "2014-06-29" @default.
- W2949366956 modified "2023-09-23" @default.
- W2949366956 title "On finiteness of curves with high canonical degree on a surface" @default.
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