On the order sequence of an embedding of the Ree curve

Abstract

In this paper we compute the Weierstrass order-sequence associated with a certain linear series on the Deligne-Lusztig curve of Ree type. As a result, we determine that the set of Weierstrass points of this linear series consists entirely of ${\mathbb{F}}_q$-rational points.

17 pages; v2: corrected typos; v3: edits in response to referee's report; submitted to Adv. Geom