Some Moduli Spaces of Bridgeland’s Stability Conditions

Abstract

We shall study some moduli spaces of Bridgeland's semi-stable objects on abelian surfaces and K3 surfaces with Picard number 1. Under some conditions, we show that the moduli spaces are isomorphic to the moduli spaces of Gieseker semi-stable sheaves. We also study the ample cone of the moduli spaces.

Verra Four-Folds, Twisted Sheaves, and the Last Involution

“…Remark 2.5. The paper [Yo] focuses mainly on moduli spaces of twisted sheaves on K3 surfaces, the above mentioned results for sheaves on abelian surfaces can be found in related works of Yoshioka [Yo2], and Minamide, Yanagide and Yoshioka [MYY,Section 4].…”

Lectures on Bridgeland Stability

“…Question 5.24 has an affirmative complete answer only for the projective plane P 2 (see [ABCH13]), P 1 × P 1 and the blow up of a point in P 2 (see [AM15]), and partial answers for other surfaces, including abelian surfaces (see [MYY14,YY14]), K3 surfaces (see [BM14a]), and Enriques surfaces (see [Nue16,Yos16]). In Section 6.6 we show how the projectivity is shown in case of P 2 via quiver representations.…”

“…We will not prove Theorem 6.34; we refer to [BM14a]. The idea of the proof, based on [MYY14], is to reduce to the case of semistable sheaves by using a Fourier-Mukai transform. The corresponding statement for non-generic stability conditions in Stab † (X) is still unknown.…”

“…The case of P 2 was studied in many articles such as [ABCH13,CHW14,LZ13,LZ16,Woo13]. The study of the abelian surfaces case started in [MM13] and was completed in [MYY14,YY14]. The case of K3 surfaces was handled in [MYY14,BM14a,BM14b].…”

“…The study of the abelian surfaces case started in [MM13] and was completed in [MYY14,YY14]. The case of K3 surfaces was handled in [MYY14,BM14a,BM14b]. Enriques surfaces were studied in [Nue16].…”