| Résume | We study boomerangs in the derived category of an elliptic curve C. These are filtrations of the zero object whose factors are polystable objects with strictly increasing phase. The numerical invariants of a boomerang are given by the Chern characters of the direct summands of these factors, which together determine a lattice polygon. When this polygon is a T-polygon, we show that the moduli space of boomerangs with a fixed collection of polystable factors is the complement of an anti-canonical embedding of C in a del Pezzo surface Z. The proof uses exceptional collections on Z, and the result has applications to the theory of q-Painlevé equations. This is joint work in progress with Tom Bridgeland and Luca Giovenzana. |
