Biduality and Reflexivity in Positive Characteristic

TL;DR

This paper extends the concepts of biduality and reflexivity to algebraic varieties over fields of positive characteristic by introducing $h$-tangent spaces, enabling reflexivity in cases where it previously failed.

Contribution

It generalizes classical reflexivity theory to positive characteristic using $h$-tangent spaces, broadening the scope of reflexivity and biduality.

Findings

Several varieties become reflexive under the new theory

The classical theory is recovered when h=0

Extended theory applies to non-ordinary reflexive varieties

Abstract

The biduality and reflexivity theorems are known to hold for projective varieties defined over fields of characteristic zero, and to fail in positive characteristic. In this article, we construct a notion of reflexivity and biduality in positive characteristic by generalizing the ordinary tangent space to the notion of $h$-tangent spaces. The ordinary reflexivity theory can be recovered as the special case $h=0$, of our theory. Several varieties that are not ordinary reflexive or bidual become reflexive in our extended theory.