On the \(X\)-ranks of points on \(\mathbb P_n\) (\(X\subset\mathbb P^n\) a curve), the tangent developable of \(X\), and the uniqueness of sets \(S\subset X\) computing \(X\)-ranks. (English) Zbl 1214.14044
Summary: Let \(X\subset\mathbb P^n\), \(n\geq 4\), be an integral projective curve. Let \(\tau(X)\subset\mathbb P^n\) be the tangent developable of \(X\). For each \(P\in\mathbb P^n\) let \(r_X(P)\) be the minimal cardinality of a set \(S\subset X\) spanning \(X\) and \({\mathcal S}(X,P)\) the set of all \(S\subset X\) computing \(r_X(P)\). Here, we give many cases with \(\sharp({\mathcal S}(X,P))=1\) and show that if \(X\) is smooth, then \(r_X(P)\geq 3\) for a general \(P\in\tau(X)\).
MSC:
| 14N05 | Projective techniques in algebraic geometry |
