Let X ⊂ ℙrK denote a variety of almost minimal degree other than a normal del Pezzo variety. Then X is the projection of a rational normal scroll X̃ ⊂ ℙr+1K from a point p ε ℙr+1K\X̃. We show that the arithmetic depth of X can be expressed in terms of the rank of the matrix M′(p), where M′ is the matrix of linear forms whose 3 × 3 minors define the secant variety of X̃.
- Depth formula
- Secant cone
- Variety of almost minimal degree
ASJC Scopus subject areas
- Applied Mathematics