On the projective normality of cyclic coverings over a rational surface

Lei Song

On the projective normality of cyclic coverings over a rational surface

Algebraic Geometry 2019-04-10 v4 Commutative Algebra

Authors: Lei Song

Abstract

Let $S$ be a rational surface with $\dim|-K_S|\ge 1$ and let $\pi: X\rightarrow S$ be a ramified cyclic covering from a nonruled smooth surface $X$ . We show that for any integer $k\ge 3$ and ample divisor $A$ on $S$ , the adjoint divisor $K_X+k\pi^*A$ is very ample and normally generated. Similar result holds for minimal (possibly singular) coverings.

Keywords

projective normality cyclic coverings rational surface adjoint divisor very ample normally generated

Cite

@article{arxiv.1612.06520,
  title  = {On the projective normality of cyclic coverings over a rational surface},
  author = {Lei Song},
  journal= {arXiv preprint arXiv:1612.06520},
  year   = {2019}
}

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On the projective normality of cyclic coverings over a rational surface

Abstract

Keywords

Cite

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