DUALITY FOR PROJECTIVE VARIETIES by ABRAMO
نویسندگان
چکیده
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
منابع مشابه
5 Homological Projective Duality
We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are Homologically Projectively Dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial c...
متن کاملAlgebraic Cocycles on Normal, Quasi-Projective Varieties
Blaine Lawson and the author introduced algebraic cocycles on complex algebraic varieties in [FL-1] and established a duality theorem relating spaces of algebraic cocycles and spaces of algebraic cycles in [FL-2]. This theorem has non-trivial (and perhaps surprising) applications in several contexts. In particular, duality enables computations of “algebraic mapping spaces” consisting of algebra...
متن کاملProjective Duality and a Chern-mather Involution
We observe that linear relations among Chern-Mather classes of projective varieties are preserved by projective duality. We deduce the existence of an explicit involution on a part of the Chow group of projective space, encoding the effect of duality on Chern-Mather classes. Applications include Plücker formulae, constraints on self-dual varieties, generalizations to singular varieties of class...
متن کاملHigher Order Duality and Toric Embeddings
The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms,...
متن کاملThe Chevalley Involution and a Duality of Weight Varieties
In this paper we show that the classical notion of association of projective point sets, [DO], Chapter III, is a special case of a general duality between weight varieties (i.e torus quotients of flag manifolds) of a reductive group G induced by the action of the Chevalley involution on the set of these quotients. We compute the dualities explicitly on both the classical and quantum levels for ...
متن کامل