## Projective manifolds with hyperplane sections being four-sheeted covers of projective space.(English)Zbl 1106.14002

Summary: Let $$L$$ be a very ample line bundle on a smooth complex projective variety $$X$$ of dimension $$\geq 6$$. We classify the polarized manifolds $$(X, L)$$ such that there exists a smooth member $$A$$ of $$|L|$$ endowed with a branched covering of degree four $$\pi \colon A \rightarrow \mathbb{P}^n$$. The cases of $$\deg \pi =2$$ and $$3$$ are already studied by A. Lanteri, M. Palleschi and A. J. Sommese [Nagoya Math. J. 137, 1–32 (1995; Zbl 0820.14005); Contemp. Math. 162, 277–292 (1994; Zbl 0841.14003)]. Recently the case of $$\deg \pi =5$$ is studied by the author.

### MSC:

 14C20 Divisors, linear systems, invertible sheaves 14H30 Coverings of curves, fundamental group 14N30 Adjunction problems

### Citations:

Zbl 0841.14003; Zbl 0820.14005
Full Text:

### References:

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