A note on property \(N_p\)
For \(M\) a very ample line bundle on a smooth complex projective variety \(Y\) and the map associated to \(M\), the author defines the property \(N_p \) for every positive integer \(p\). The problem under consideration is: Given \(M\), a line bundle as before on \(Y\) satisfying property \(N_p,\) and fixing a natural number \(s \), for which \(k\) does the line bundle \(M^s \) satisfy the property \(N_k \)? The author proves (proposition 1) that if \(M\) satisfies property \(N_p \) then \(M^s \) satisfies property \(N_x\) where \( x= \min \{ s,p\} \).
line bundle on a smooth complex projective variety
scientific article; zbMATH DE number 1463439