Stability conditions on $K3$ surfaces

By T. Bridgeland. 2003

480 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d6cb51132e664f7b1de61d9324def3a41570db14

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lectures on Bridgeland Stability (2016, methodology): “This is explained in detail in the case of K3 surfaces in [Bri08], and can be directly deduced from [Bri07, Sections 6 & 7].”
Stability conditions for generic K3 categories (2006, methodology): “now either be obtained by following the general approach in [ 6 ] or by a more direct argument given below, which does not rely on the description of Stab(X) in Theorem 4.8.”
Moduli stacks and invariants of semistable objects on K3 surfaces (2007, methodology): “Here we collect some basic definitions and results in [7], [ 6 ].”
A categorical invariant for cubic threefolds (2009, methodology): “hat N(TY ) is the right orthogonal complement of the classes [OY ] and [OY (1)]. Hence N(TY ) ∼= Z⊕2. We have χ(Il,Il) = χ(S T Y (Il),S T Y (Il)) = χ(Il,S T Y (Il)) = −1. By [16, Cor. 4.4], S3 T Y ∼= [5] and so χ(S T Y (Il),Il) = χ(Il,S2T Y (Il)) = χ(Il,S−1 T (Il)[5]) = χ(S T Y (Il),Il[5]) = −χ(S T ”
Stability Manifold of P^1 (2004, unknown): “A G ] 1 9 M ar”
Stability conditions and extremal contractions (2012, methodology): “ral charge Zf∗ω is given by Zf∗ω(E) = − Z X (2) e−if∗ωch(E), and the heart Bf∗ω is a tilting of the perverse heart Per(X/Y) in the sense of [10]. The tilting here is similar to the one constructed in [12], [1] applied for Coh(X). Then we deform σ 0 to a one parameter family {σt}t∈(−1,1), so that any”
Gluing Stability Conditions (2009, background): “Note that this corollary implies that all (locally finite) stability conditions constructed in [2, 4, 5, 11] are reasonable.”
Projectivity and birational geometry of Bridgeland moduli spaces on an Enriques surface (2014, background): “phic to Y itself if gcd(r,c,2s) = 2. 4. Review: Stabilityconditions onK3 andEnriques surfaces In this section we give a brief review of Bridgeland’s results on stability conditions for K3 surfaces in [Bri08], and of results by Toda, Yoshioka and others related to moduli spaces of Bridgeland-stable o”
Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities (2011, methodology): “4]) to the notion of a “full” stability condition introduced in [Bri08]; in particular:”
Inducing stability conditions (2007, background): “ained in a G-invariant connected subset of Stab† N(D b(X)).) Remark 3.2. (i) It is perhaps worth noticing that Stab† N(D b(Y)) could be alternatively obtained by repeating the same construction as in [7] for Enriques surfaces. Since we will not need this in the sequel, the easy check is left to the ”
MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations (2013, background): “ of the Brauer class α. Deﬁnition 2.8. A (full, numerical) stability condition on (X,α) is a Bridgeland stability condition on Db(X,α), whose lattice Λ is given by the Mukai lattice H∗ alg(X,α,Z). In [Bri08], Bridgeland describes a connected component of the space of numerical stability conditions o”
Lectures on K3 Surfaces (2016, background): “A conjecture of Bridgeland [84] describes it as a fundamental group.”
Stability conditions and crepant small resolutions (2005, methodology): “In general Stab(D) is infinite dimensional, so we usually consider only numerical stability conditions as in [5], [7].”