Geometric stability conditions under autoequivalences and applications: Elliptic surfaces

Jason Lo; Cristian Mauricio Martinez Esparza

doi:10.1016/j.geomphys.2023.104994

Geometric stability conditions under autoequivalences and applications: Elliptic surfaces

Jason Lo
, Cristian Mauricio Martinez Esparza

Research output: Contribution to Journal › Research Article › peer-review

2 Scopus citations

Abstract

On a Weierstraß elliptic surface, we describe the action of the relative Fourier-Mukai transform on the geometric chamber of Stab(X), and in the K3 case we also study the action on one of its boundary components. Using new estimates for the Gieseker chamber we prove that Gieseker stability for polarizations on certain Friedman chamber is preserved by the derived dual of the relative Fourier-Mukai transform. As an application of our description of the action, we also prove projectivity for some moduli spaces of Bridgeland semistable objects.

Original language	English (US)
Journal	Journal of Geometry and Physics
Volume	194
DOIs	https://doi.org/10.1016/j.geomphys.2023.104994
State	Published - Dec 2023

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All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

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10.1016/j.geomphys.2023.104994

Cite this

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title = "Geometric stability conditions under autoequivalences and applications: Elliptic surfaces",

abstract = "On a Weierstra{\ss} elliptic surface, we describe the action of the relative Fourier-Mukai transform on the geometric chamber of Stab(X), and in the K3 case we also study the action on one of its boundary components. Using new estimates for the Gieseker chamber we prove that Gieseker stability for polarizations on certain Friedman chamber is preserved by the derived dual of the relative Fourier-Mukai transform. As an application of our description of the action, we also prove projectivity for some moduli spaces of Bridgeland semistable objects.",

author = "Jason Lo and Esparza, \{Cristian Mauricio Martinez\}",

year = "2023",

month = dec,

doi = "10.1016/j.geomphys.2023.104994",

language = "English (US)",

volume = "194",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier BV",

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TY - JOUR

T1 - Geometric stability conditions under autoequivalences and applications: Elliptic surfaces

AU - Lo, Jason

AU - Esparza, Cristian Mauricio Martinez

PY - 2023/12

Y1 - 2023/12

N2 - On a Weierstraß elliptic surface, we describe the action of the relative Fourier-Mukai transform on the geometric chamber of Stab(X), and in the K3 case we also study the action on one of its boundary components. Using new estimates for the Gieseker chamber we prove that Gieseker stability for polarizations on certain Friedman chamber is preserved by the derived dual of the relative Fourier-Mukai transform. As an application of our description of the action, we also prove projectivity for some moduli spaces of Bridgeland semistable objects.

AB - On a Weierstraß elliptic surface, we describe the action of the relative Fourier-Mukai transform on the geometric chamber of Stab(X), and in the K3 case we also study the action on one of its boundary components. Using new estimates for the Gieseker chamber we prove that Gieseker stability for polarizations on certain Friedman chamber is preserved by the derived dual of the relative Fourier-Mukai transform. As an application of our description of the action, we also prove projectivity for some moduli spaces of Bridgeland semistable objects.

UR - http://dx.doi.org/10.1016/j.geomphys.2023.104994

U2 - 10.1016/j.geomphys.2023.104994

DO - 10.1016/j.geomphys.2023.104994

M3 - Research Article

SN - 0393-0440

VL - 194

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

Geometric stability conditions under autoequivalences and applications: Elliptic surfaces

Abstract

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