The Betti table of a high degree curve is asymptotically pure

Abstract

We prove that asymptotically in the degree, the main term of the Boij--Söderberg decomposition of a high degree curve is a single pure diagram that only depends on the genus of the curve. This answers a question of Ein and Lazarsfeld in the case of curves.

6 pages. Dedicated to Rob Lazarsfeld on the occasion of his sixtieth birthday. This version corrects a typo and adds a few clarifying details in the proof of Theorem 2.3