Properness for scaled gauged maps

Eduardo González; Pablo Solis; Chris T. Woodward

doi:10.1016/j.jalgebra.2017.06.015

Properness for scaled gauged maps

Eduardo González
, Pablo Solis
, Chris T. Woodward

Mathematics

California Institute of Technology
Rutgers - The State University of New Jersey, New Brunswick

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

Abstract

We prove properness of moduli stacks of gauged maps satisfying a stability condition introduced by Mundet [40], Schmitt [46] and Ziltener [57]. The proof combines a git construction of Schmitt [46], properness for twisted stable maps by Abramovich–Vistoli [1], a variation of a boundedness argument due to Ciocan–Fontanine–Kim–Maulik [13], and a removal of singularities for bundles on surfaces in Colliot–Thélène–Sansuc [14].

Original language	English
Pages (from-to)	104-157
Number of pages	54
Journal	Journal of Algebra
Volume	490
DOIs	https://doi.org/10.1016/j.jalgebra.2017.06.015
State	Published - Nov 15 2017

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Equivariant and gauged Gromov–Witten theory
Git quotients
Lie theory

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10.1016/j.jalgebra.2017.06.015

Cite this

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title = "Properness for scaled gauged maps",

abstract = "We prove properness of moduli stacks of gauged maps satisfying a stability condition introduced by Mundet [40], Schmitt [46] and Ziltener [57]. The proof combines a git construction of Schmitt [46], properness for twisted stable maps by Abramovich{\textendash}Vistoli [1], a variation of a boundedness argument due to Ciocan{\textendash}Fontanine{\textendash}Kim{\textendash}Maulik [13], and a removal of singularities for bundles on surfaces in Colliot{\textendash}Th{\'e}l{\`e}ne{\textendash}Sansuc [14].",

keywords = "Equivariant and gauged Gromov{\textendash}Witten theory, Git quotients, Lie theory",

author = "Eduardo Gonz{\'a}lez and Pablo Solis and Woodward, \{Chris T.\}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = nov,

day = "15",

doi = "10.1016/j.jalgebra.2017.06.015",

language = "English",

volume = "490",

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journal = "Journal of Algebra",

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TY - JOUR

T1 - Properness for scaled gauged maps

AU - González, Eduardo

AU - Solis, Pablo

AU - Woodward, Chris T.

PY - 2017/11/15

Y1 - 2017/11/15

N2 - We prove properness of moduli stacks of gauged maps satisfying a stability condition introduced by Mundet [40], Schmitt [46] and Ziltener [57]. The proof combines a git construction of Schmitt [46], properness for twisted stable maps by Abramovich–Vistoli [1], a variation of a boundedness argument due to Ciocan–Fontanine–Kim–Maulik [13], and a removal of singularities for bundles on surfaces in Colliot–Thélène–Sansuc [14].

AB - We prove properness of moduli stacks of gauged maps satisfying a stability condition introduced by Mundet [40], Schmitt [46] and Ziltener [57]. The proof combines a git construction of Schmitt [46], properness for twisted stable maps by Abramovich–Vistoli [1], a variation of a boundedness argument due to Ciocan–Fontanine–Kim–Maulik [13], and a removal of singularities for bundles on surfaces in Colliot–Thélène–Sansuc [14].

KW - Equivariant and gauged Gromov–Witten theory

KW - Git quotients

KW - Lie theory

UR - https://www.scopus.com/pages/publications/85025825612

UR - https://www.scopus.com/pages/publications/85025825612#tab=citedBy

U2 - 10.1016/j.jalgebra.2017.06.015

DO - 10.1016/j.jalgebra.2017.06.015

M3 - Article

AN - SCOPUS:85025825612

SN - 0021-8693

VL - 490

SP - 104

EP - 157

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Properness for scaled gauged maps

Abstract

ASJC Scopus Subject Areas

Keywords

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