Stability conditions on K3 surfaces

Abstract

This paper contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K3 surface.

Lectures on Bridgeland Stability

“…The main result is the following (see [Bri08,AB13,BM11]). We will choose Λ = K num (X) and v as the Chern character map as in Example 5.7.…”

“…It is equivalent to Bridgeland's notion of a full locally-finite stability condition in [Bri08,Definition 4…”

“…For a detailed account of the general theory of tilting we refer to [HRS96] and [BvdB03, Section 5]. The idea of using this operation to construct Bridgeland stability conditions is due to Bridgeland in [Bri08], in the case of K3 surfaces. The extension to general smooth projective surfaces is in [AB13].…”

“…In Section 6 we construct stability conditions σ ω,B for each choice of ample R-divisor class ω and arbitrary R-divisor class B. This construction originated in [Bri08] in the case of K3 surfaces. Arcara and Bertram realized that the construction can be generalized to any surface by using the Bogomolov Inequality in [AB13].…”

“…If we fix a numerical class v, it turns out that semistable objects with class v vary nicely within Stab(X) due to [Bri08]. More precisely, there is a locally finite wall and chamber structure such that the set of semistable objects with class v is constant within each chamber.…”