DUALITY FOR PROJECTIVE VARIETIES by ABRAMO

We develop the theory of duality for projective varieties defined over fields of arbitrary characteristic. A central concept in this work is that of reflexivity and our main tool is the rank of certain local Hessians which provides a numerical criterion for reflexivity. Many of our results are necessary and sufficient conditions for reflexivity. We also analyze the reflexivity of a general hypersurface section of a given variety. Toward the classification of non-reflexive varieties, we determine all smooth in codimension one hypersurfaces with rank zero local Hessians and we solve the classification problem for a special class of these varieties. Thesis Supervisor: Steven L. Kleiman Title: Professor of Mathematics