Interpolation in higher codimension

Abstract Following the suggestions contained in [5], I will discuss constructions that generalizes the interpolation problems for divisors to the case of varieties of higher codimension, with emphasis on the case of curves arising as 0-loci of vector bundles of rank 2 in $$\mathbb {P}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> .