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

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 $h^1({\mathcal{O}}_S(1))>0$. 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.

arXiv comment20 pages. Final version. To appear in Math. Scand

References in corpus (2)

• Surfaces of Degree 10 in the Projective Fourspace via Linear Systems and Linkage
• Rational surfaces in P^4 containing a plane curve