---
abstract: '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.'
address: |
    Institut für Mathematik\
    Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
author:
- Elisa Gorla
title: Lifting the determinantal property
---

Introduction {#introduction .unnumbered}
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Standard and good determinantal schemes are a large family of projective schemes, to which belong many varieties that have been classically studied. For example rational normal scrolls, rational normal curves, and some Segre varieties are good determinantal schemes. Standard determinantal schemes are cut out by the maximal minors of a matrix of polynomials (see Definition \[stdef\]). In particular they are arithmetically Cohen-Macaulay, and their saturated ideal is resolved by the Eagon-Northcott complex. Good determinantal schemes are standard determinantal schemes that are locally a complete intersection outside a subscheme. Ideals of minors have been 