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

• Autores: Abdul M. Mohamad
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 119, Nº 2, 2016, págs. 169-196
• Idioma: inglés
• DOI: 10.7146/math.scand.a-24742
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• Resumen

  • 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.