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

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

2011-03-21

arxiv.org/abs/1103.4116v1

Mathematics

Algebraic Geometry

Scientific paper

The aim of this paper is to present a construction of a linearly normal smooth rational surface of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special. Our construction is done via linear systems. In particular, we give open and closed conditions for the configuration of points. We also present a short list of linear systems whom are the only possibilities for other families of surfaces with the prescribed numerical invariants.

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