Some moduli spaces of Bridgeland's stability conditions

By Hiroki Minamide, S. Yanagida, K. Yoshioka. 2011

62 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ae035a3413b11b4eb4fb16ddb8474ba83ba73e51

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Bridgeland’s stabilities on abelian surfaces (2012, background): “ian surfaces, the studies on the dependence of the parameters, i.e., those of wall and chamber structures, are started by two groups Maciocia and Meachan [5], and Minamide, Yanagida and Yoshioka [7], [8]. In this paper, we continue our study on the wall and chamber structures. In particular, we shal”
Lectures on Bridgeland Stability (2016, methodology): “The idea of the proof, based on [MYY14], is to reduce to the case of semistable sheaves by using a Fourier-Mukai transform.”
A generalized Bogomolov–Gieseker inequality for the three-dimensional projective space (2012, background): “It would be very interesting to study how moduli spaces of Bridgeland semistable objects vary when varying the stability condition (very much like the situation described in [Arcara et al. 2013; Maciocia and Meachan 2013; Lo and Qin 2011; Minamide et al. 2011; Yanagida and Yoshioka 2012; Bayer and M”
Projectivity and birational geometry of Bridgeland moduli spaces (2012, unknown): “The analog of Theorem 1.3 for abelian surfaces has been proved in [66]; a diﬀerent method to prove projectivity was established in [53,54].”
Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces (2012, background): “In the case of abelian surfaces and K3 surfaces this implies that such moduli spaces are projective varieties and represent the appropriate moduli functor (see [MM11] and [MYY11b] for special cases of this).”
MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations (2013, methodology): “.5. 8. ISOTROPIC WALLS ARE UHLENBECK WALLS In this section, we study potential walls W in the case where H admits an isotropic class w∈ H,w2 = 0. Following an idea of Minamide, Yanagida, and Yoshioka [MYY11b], we study the wall W via a Fourier-Mukai transform after whichwbecomes the class of a point”
The integral Hodge conjecture for two-dimensional Calabi–Yau categories (2020, background): “3] (based on [96, 69]) but the case of general α holds by similar arguments.”