In this note we study standard and in particular 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 transference of the property of being standard or good determinantal under basic double linkage.
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