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arXiv · 1103.4116

Smooth rational surfaces of $d=11$ and $π=8$ in $\mathbb{P}^5$

Abdul Moeed Mohammad
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Abstract

We construct a linearly normal smooth rational surface S of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our construction is done via linear systems and we describe the configuration of points blown up in the projective plane. We also present a short list, generated by the adjunction mapping, of linear systems whom are the only possibilities for other families of surfaces with the prescribed numerical invariants.

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Abdul Moeed Mohammad. 2016-09-05. Smooth rational surfaces of $d=11$ and $π=8$ in $\mathbb{P}^5$. https://doi.org/10.7146/math.scand.a-24742

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