The Corrado Segre Archive

Universal Properties of the Corrado Segre Embedding

Let S(Π0,Π1) be the product of the projective spaces Π0 and Π1, i.e. the semilinear space whose point set is the product of the point sets of Π0 and Π1, and whose lines are all products of the kind {P0}×g1 or g0×{P1}, where P0, P1 are points and g0, g1 are lines. An embedding χ : S(Π0,Π1) → Π′ is an injective mapping which maps the lines of S(Π0,Π1) onto (whole) lines of Π′. The classical embed...

Corrado Segre and Nodal Cubic Threefolds

We discuss the work of Corrado Segre on nodal cubic hypersurfaces with emphasis on the cases of 6-nodal and 10-nodal cubics. In particular we discuss the Fano surface of lines and conic bundle structures on such threefolds. We review some of the modern research in algebraic geometry related to Segre’s work.

Corrado Priami

The Segre Embedding

Throughout this note all rings are commutative, and A is a fixed ring. If S, T are graded A-algebras then the tensor product S ⊗A T becomes a graded A-algebra in a canonical way with the grading given by (TES,Lemma 13). That is, S ⊗A T is the coproduct of the morphisms of A-modules Sd ⊗A Te −→ S ⊗A T for d, e ≥ 0. The canonical morphisms p1 : S −→ S ⊗A T, p2 : T −→ S ⊗A T are then morphisms of ...

A Response to Roesch and Corrado