Lectures on Bridgeland Stability

Macrì, Emanuele; Schmidt, Benjamin

doi:10.1007/978-3-319-59486-6_5

Cited by 55 publications

(39 citation statements)

References 89 publications

(112 reference statements)

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“…For every (α, β) ∈ R >0 × R, there exists a Bridgeland stability condition σ α,β = (Coh β (S), Z α,β ) (see [14,Section 6], or [2] for the original treatment), where:…”

Section: The (˛ ˇ)-Plane Of a Polarized Abelian Surfacementioning

confidence: 99%

The basepoint-freeness threshold of a very general abelian surface

Rojas

2022

Sel. Math. New Ser.

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For abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepoint-freeness threshold. Our main tool is the relation between cohomological rank functions and Bridgeland stability. In virtue of recent results of Caucci and Ito, these computations provide new information on the syzygies of polarized abelian surfaces.

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“…For every (α, β) ∈ R >0 × R, there exists a Bridgeland stability condition σ α,β = (Coh β (S), Z α,β ) (see [14,Section 6], or [2] for the original treatment), where:…”

Section: The (˛ ˇ)-Plane Of a Polarized Abelian Surfacementioning

confidence: 99%

The basepoint-freeness threshold of a very general abelian surface

Rojas

2022

Sel. Math. New Ser.

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“…For example, this is true for the moduli spaces of vector bundles over many classes of surfaces (see [16,54,48,43,17,19,22] or surveys [21,35,44]).…”

Section: Introductionmentioning

confidence: 99%

On the First Steps of the Minimal Model Program for the Moduli Space of Stable Pointed Curves

Codogni¹,

Tasin²,

Viviani³

2021

J. Inst. Math. Jussieu

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The aim of this paper is to study all the natural first steps of the minimal model program for the moduli space of stable pointed curves. We prove that they admit a modular interpretation, and we study their geometric properties. As a particular case, we recover the first few Hassett–Keel log canonical models. As a by-product, we produce many birational morphisms from the moduli space of stable pointed curves to alternative modular projective compactifications of the moduli space of pointed curves.

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“…Roughly speaking, a stability condition σ on a triangulated category T consists of data (Z, P) where Z is called the central charge, and P is a slicing on T . There are many examples and conjectures about the constructions of the stability conditions, we refer to surveys [3,4,5] for more information and applications.…”

Section: Introductionmentioning

confidence: 99%