Examples of smooth non-general type surfaces in P^4

Details Examples of smooth non-general type surfaces in P^4 Examples of smooth non-general type surfaces in P^4

1997-03-05

arxiv.org/abs/alg-geom/9703006v2

Mathematics

Algebraic Geometry

Paper written in 1994. Final version to appear in the Proceedings of the London Mathematical Society 20 pages, AMSTeX v2.1 wit

Scientific paper

The aim of the paper is to provide a series of new examples of smooth surfaces in P^4, not of general type, in degrees varying from 12 up to 14, and to describe their geometry. By using mainly syzygies and liaison techniques, we construct the following families of surfaces: - minimal proper elliptic surfaces of degree 12 and sectional genus 13, - two types of non-minimal proper elliptic surfaces of degree 12 and sectional genus 14, - non-minimal K3 surfaces of degree 13 and sectional genus 16, and - non-minimal K3 surfaces of degree 14 and sectional genus 19.

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