Bridgeland’s stabilities on abelian surfaces

By S. Yanagida, K. Yoshioka. 2012

50 citations recorded by the source corpus.

In this paper, we shall study the structure of walls for Bridgeland’s stability conditions on abelian surfaces. In particular, we shall study the structure of walls for the moduli spaces of rank 1 complexes on an abelian surface with the Picard number 1.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/39f2a9f274b80268e85df1b330632093027acf3d

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In Geometry and Topology

1. Emanuele Macrì
2. D. Huybrechts
3. Benjamin Schmidt
4. K. Yoshioka
5. P. Stellari
6. Arend Bayer
7. M. Shen
8. E. Markman

In Mathematical Physics

1. D. Huybrechts
2. Emanuele Macrì
3. Benjamin Schmidt
4. K. Yoshioka
5. M. Shen
6. L. Fu
7. P. Stellari
8. Charles Vial

Citations in the corpus

• 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”
• Bridgeland's stability and the positive cone of the moduli spaces of stable objects on an abelian surface (2012, background): “ors v±. For a Mukai vector v= (r,dH,a), we show that v± are not defined over Qif and only if p hv2i/(H2) ∈ Q. For the rank 1 case, this condition is equivalent to the existence of infinitely many walls [28]. According to Markman’s solution [14] of the movable cone conjecture of Kawamata and Morrison (”
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, background): “tion v(E) := ch(E) · √ td Y. It is an element of H(A) by construction. AssumethatAadmitsstabilityconditionsinthesenseofBridgeland[Bri07];thishasbynow been established for examples (i) ∼ (iii) [Bri08] [YY14] [BLM+17] [PPZ19], and is also expected for example (iv). We denote the distinguished connecte”
• A generalized Bogomolov–Gieseker inequality for the smooth quadric threefold (2013, background): “Examples of successful applications are found in the birational geometry of Hilbert schemes of points on smooth projective surfaces (see, for example, [2, 4, 15, 22]).”
• Lectures on K3 Surfaces (2016, background): “See [264] for some comments and references and the recent preprints [40, 41, 637].”