  In this note we study standard and good determinantal schemes. We show that
there exist arithmetically Cohen-Macaulay schemes that are not standard
determinantal, and whose general hyperplane section is good determinantal. We
prove that if a general hyperplane section of a scheme is standard (resp. good)
determinantal, then the scheme is standard (resp. good) determinantal up to
flat deformation. We also study the transfer of the property of being standard
or good determinantal under basic double links.

Commutative Algebra;Algebraic Geometry