Bridgeland-stable moduli spaces for $K$-trivial surfaces

By D. Arcara, Aaron Bertram, Max Lieblich. Journal of the European Mathematical Society (Print), 2007

218 citations recorded by the source corpus.

It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca9a35d81e4f5a574a2fec2fee96a899594beaf6

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Some moduli spaces of Bridgeland's stability conditions (2011, background): “rface with Pic(X) = ZH. Assume that (β,ω) is general. There is a coarse moduli scheme M(β,ω)(v) which is isomorphic to the projective scheme MHb(u), where u= Φ(v). In particular, the moduli spaces in [AB] are projective, if ωis general. Remark 4.1.2. Maciocia and Meachan showed the claim for v= 1+2H”
The space of stability conditions on the local projective plane (2009, background): “Some examples of stability conditions on projective spaces were studied in [Mac07, ABL07 , Ohk08].”
Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds (2013, background): “Let the abelian category Bω,B = 〈Fω,B [1],Tω,B〉 ⊂ D(X) be the corresponding tilt of Coh(X).”
The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds (2014, background): “Then F or F[1] is a νω,B-stable object of CohH,B(X).”
Stability conditions and extremal contractions (2012, methodology): “duli spaces of (semi)stable objects after crossing the above boundary (wall). Indeed, the stability conditions σt for t < 0 are contained in the geometric chamber constructed by Arcara and Bertram [1], and σ 0 lies at its boundary corresponding to the pull-back of the ample cone of Y to X. The st”
Lectures on Bridgeland Stability (2016, methodology): “r class B. This construction originated in [Bri08] in the case of K3 surfaces. Arcara and Bertram realized that the construction can be generalized to any surface by using the Bogomolov Inequality in [AB13]. The proof of the support property is in [BM11, BMT14, BMS16]. As a consequence, these stabil”
Bridgeland’s stabilities on abelian surfaces (2012, result): “ suﬃcient to show the independence of σ(β,ω)-semi-stability, where (β,L) ∈V ×U. We set X1 := MH(r1eγ). For a universal family E on X×X1 as a twisted object, we consider the FourierMukai transform ΦE ∨[1] X→X1. Then we have an isomorphism M(β,ω)(v) →Mωe(u) ss, where u := ΦE ∨[1] X→X1(v). Since (c1(ue”