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arXiv · 1706.05734

Lines on smooth polarized $K3$-surfaces

Alex Degtyarev
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Abstract

For each integer $D\ge3$, we give a sharp bound on the number of lines contained in a smooth complex $2D$-polarized $K3$-surface in $\mathbb{P}^{D+1}$. In the two most interesting cases of sextics in $\mathbb{P}^4$ and octics in $\mathbb{P}^5$, the bounds are $42$ and $36$, respectively, as conjectured in an earlier paper.

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Alex Degtyarev. 2017-08-17. Lines on smooth polarized $K3$-surfaces. https://doi.org/10.1007/s00454-018-0038-5

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