SOME SPECIAL PROPERTIES OF THE ADJUNCTION THEORY FOR 3-FOLDS IN P-5

This paper studies the adjunction theory of smooth 3-folds in P-5. Bec ause of the many special restrictions on such 3-folds the structure of the adjunction theoretic reductions are especially simple, e.g., the 3-fold equals its first reduction, the second reduction is smooth exce pt possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of i ts second reduction are very explicit. Tables summarizing the classifi cation of such 3-folds up to degree 12 are included. Many of the gener al results in this article are shown to hold for smooth projective n-f olds embedded in P-N with N less than or equal to 2n - 1.