Stability conditions for generic K3 categories

By D. Huybrechts, Emanuele Macrì, P. Stellari. Compositio Mathematica, 2006

86 citations recorded by the source corpus.

Abstract A K3 category is by definition a Calabi–Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no spherical objects (or just one up to shift). We study stability conditions on K3 categories as introduced by Bridgeland and prove his conjecture about the topology of the stability manifold and the autoequivalences group for generic twisted projective K3, abelian surfaces, and K3 surfaces with trivial Picard group.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbddd7096583a8c33f174eb2b9903cbf7af38371

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In Geometry and Topology

1. Emanuele Macrì
2. P. Stellari
3. Arend Bayer
4. D. Huybrechts
5. Sukhendu Mehrotra
6. Chunyi Li
7. Benjamin Schmidt
8. Yukinobu Toda

In Mathematical Physics

1. Emanuele Macrì
2. P. Stellari
3. Arend Bayer
4. D. Huybrechts
5. Sukhendu Mehrotra
6. Chunyi Li
7. Yukinobu Toda
8. Alexander Kuznetsov

Citations in the corpus

• Polynomial Bridgeland stability conditions and the large volume limit (2007, background): “[MMS07] Emanuele Macri, Sukhendu Mehrotra, and Paolo Stellari.”
• Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces (2018, background): “ contained in only one connected component of P0 and that η−1(P0) is connected and simply-connected as well. This is known only for generic analytic K3 surfaces (and some generic twisted K3 surfaces) [HMS08]; in the algebraic case, the strongest evidence is [BB17]. This is related to the choice of a”
• Lectures on K3 Surfaces (2016, methodology): “Note that the same techniques were used in [265] to determine Aut(Db(X)) for the generic fibre of the generic formal deformation of a projective K3 surface, which is the key to Corollary 3.”
• Projectivity and birational geometry of Bridgeland moduli spaces (2012, unknown): “As proven in [32, Section 3.1], the results stated in this section extend without any difference to the case of twisted K3 surfaces: Let ( X, α ) be a twisted K3 surface, α ∈ Br( X ).”
• Inducing stability conditions (2007, methodology): “... stability conditions for derived categories of coherent sheaves on low-dimensional projective manifolds, due, in large part, to the intuition that these stability manifolds should be (approximate) mathematical models of the physicists’ stringy K¨ahler moduli space (see [11] and [14]), and also b”
• The space of stability conditions on the local projective plane (2009, background): “fundamental difference to the case of Calabi-Yau 2-categories (as studied in [Bri08, Tho08, Bri05a, IUU06, HMS08 ]).”