Smooth Rational Surfaces Of $d=11$ And $\pi=8$ In $\mathbb{P}^5$

  • Abdul Moeed Mohammad


We construct a linearly normal smooth rational surface $S$ of degree $11$ and sectional genus $8$ in the projective five space. 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. Using the theory of adjunction mappings, we present a short list of linear systems which are the only possibilities for other families of surfaces with the prescribed numerical invariants.
How to Cite
Mohammad, A. M. (2016). Smooth Rational Surfaces Of $d=11$ And $\pi=8$ In $\mathbb{P}^5$. MATHEMATICA SCANDINAVICA, 119(2), 169-196.