On flexes of the Kummer variety (Note on a theorem of R. C. Gunning)

Abstract

In his paper (3), R.C. Gunning has given a new characterization of Jacobi varieties among all princlpally polarized aballan varieties, by using trisecants of the associated Kummer variety. The present paper is motivated by the llnk between Gunning’s results and the -as yet unanswered- question about the Novikov Hypothesis. Our main statement is Theorem (3.1), which ia just a more general versión of the key result of [3], allowing also limit cases of the original assumptions. Section 3 is devoted to the proof of this statement. In particular, one obtains similar characterizations of jacobians by means of flexes instead of trisecants (cf Section 1).