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The genus of space curves and Bridgeland stability
ÕªÒª£º In this talk, we will give an estimation for the arithmetic genus of an integral space curve, which are not contained in a surface of degree $k-1$. Our main technique is the Bogomolov-Gieseker type inequality for $\mathbb{P}^3$ which naturally appears in the construction of the Bridgeland stability conditions on threefolds.