Smooth Rational Surfaces Of d=11 And π=8 In P^5 - Mohammad, Abdul Moeed (MATHEMATICA SCANDINAVICA, 2016)
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(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.