This work studies the adjunction theory of smooth $3$-folds in $\mathbb P^5$. Because 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 except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given $3$-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such $3$-folds up to degree $12$ are included. Many of the general results are shown to hold for smooth projective $n$-folds embedded in $\mathbb P^N$ with $N \leq 2n-1$.

Some Special Properties of the Adjunction Theory for 3-Folds in P5 (Memoirs of the American Mathematical Society)

Science & Math

Schneider, Michael

Sommese, Andrew John

Beltrametti, Mauro

Mathematics

Amer Mathematical Society

<p>Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.</p>

NUMERICAL SOLUTION OF SYSTEMS OF POLYNOMIALS ARISING IN ENGINEERING AND SCIENCE, THE

Wampler II, Charles W.

Charles W. Wampler II

World Scientific Pub Co Inc

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