Some Examples of Smooth Non General Type Surfaces in P4

Boundedness for surfaces in weighted P

Ellingsrud and Peskine (1989) proved that there exists a bound on the degree of smooth non general type surfaces in P. The latest proven bound is 52 by Decker and Schreyer in 2000. In this paper we consider bounds on the degree of a quasismooth non-general type surface in weighted projective 4-space. We show that such a bound in terms of the weights exists, and compute an explicit bound in simp...

Irregular Elliptic Surfaces of Degree 12 in the Projective Fourspace

The purpose of this paper is to give two different constructions of irregular surfaces of degree 12 in P4. These surfaces are new and of interest in the classification of smooth non-general type surfaces in P4. This classification problem is motivated by the theorem of Ellingsrud and Peskine [9] which says that the degree of smooth non-general type surfaces in P4 is bounded. Moreover the new fa...

On surfaces in P with no trisecant lines

Examples of surfaces in P6 with no trisecant lines are constructed. A classification recovering them is given and conjectured to be the complete one. Introduction The study of varieties embedded in P with no trisecant lines is a very classical problem in algebraic geometry. The simplest case, i.e. the case of space curves goes back to Castelnuovo. For surfaces the problem has been studied in co...

EXAMPLES OF SMOOTHNON - GENERAL TYPE SURFACES IN P 4 Sorin

Smooth projective varieties with small invariants have got renewed interest in recent years, primarily due to the ne study of the adjunction mapping by Reider, Sommese, Van de Ven and others. For the special case of smooth surfaces in P 4 the method goes back to the Italian geometers, who at the turn of the century used it for the study of the surfaces of degree less than 7, or sectional genus ...

Non-general Type Surfaces in P4: Some Remarks on Bounds and Constructions