Generation and syzygies of the first secant variety

Abstract

Under certain effective positivity conditions, we show that the secant variety to a smooth variety satisfies $N_{3,p}$. For smooth curves, we provide the best possible effective bound on the degree $d$ of the embedding, $d\ge 2g+3+p$.

There was an error in version 2. The degree bound for curves has been re-established, but the proof in higher dimensions has not yet been fixed. See note at the beginning of this version

References in corpus (1)

• Osculating Varieties of Veronesean and their higher secant varieties