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Keywords:
space curve; arithmetic genus; Bridgeland stability; Bogomolov-Gieseker inequality
space curve; arithmetic genus; Bridgeland stability; Bogomolov-Gieseker inequality
Summary:
We give an estimation for the arithmetic genus of an integral space curve which is not contained in a surface of degree $k-1$. Our main technique is the Bogomolov-Gieseker type inequality for $\mathbb {P}^3$ proved by Macrì.
References:
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