Gorenstein liaison, complete intersection liaison invariants and unobstructedness

This paper contributes to the liason and obstruction theory of subschemes i n P-n having codimension at least three The first part establishes several basic results on Gorenstein liaison. A c lassical result of Gaeta on liaison classes of projectively normal curves i n P-3 is generalized to the statement that every codimension c "standard de terminantal scheme" (i.e. a scheme defined by the maximal minors of a t x ( t + c - 1) homogenous matrix), is in the Gorenstein liaison class of a (G-l iaison) theory is developed as, a theory of generalized divisors om arithme tically Cohen-Macaulay schemes. In particular, a rather general constructio n of basic double G-linkage is introduced, which preserves the even G-liais on class. This construction extends the notion of basic double linkage, whi ch plays a fundamental role in the codimension two situation. The second part of the paper studies groups which are invariant under compl ete intersection linkage, and give: invariants. Several differences between son are highlighted. For example, it smooth arithmetically Cohen-Macaulay subscheme belong, in general, to different complete intersection liaison cl assed even Gorenstein liaison class. The third part develops the int interplay between liason theory and obstruc tion theory and includes dimension estimates of various Hilbert schemes. Fo r example, it is shown that most standard do determinantal subschemes of co dimension 3 are unobstructed, and the dimensions of their components in the corresponding Hilbert schemes are computed.