Different Hearts on Elliptic Curves

Abstract

The classical Mumford stability condition of vector bundles on a complex elliptic curve X, can be viewed as a Bridgeland stability condition on D^b (Coh X), the bounded derived category of coherent sheaves on X. This point of view gives us infinitely many t-structures and hearts on D^b (Coh X). In this paper, we answer the question which of these hearts are Noetherian or Artinian.