Stable gauged maps

Solis, Pablo; Woodward, Chris

doi:10.1090/pspum/097.1/09

Cited by 3 publications

(3 citation statements)

References 58 publications

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“…The theory of decorated vector bundles that we have just outlined is closely related to the theory of stable gauged maps which has been used in quantum cohomology. We refer to [7] for an introduction.…”

Section: The Actionmentioning

confidence: 99%

Notes on coherent systems

Schmitt

2020

RMTA

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Section: The Actionmentioning

confidence: 99%

Notes on coherent systems

Schmitt

2020

RMTA

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“…For (+), if we change the problem by instead insisting that the points are distinct, then a beautiful answer is given by the moduli space Q n of 'stable scaled marked curves' constructed by Mau and Woodward as a projective variety [MW10], after Ziltener constructed it with symplectic methods [Zi06,Zi14]. The moduli space Q n plays a central role in the context of gauged stable maps [Wo15,GSW17,GSW18]. The first goal of this paper is to construct a compactification P n (related to Q n but simpler) which answers (+) as stated above.…”

Section: Introductionmentioning

confidence: 99%

Configurations of points on a line up to scaling or translation

Zahariuc¹

2021

Preprint

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We prove that the Losev-Manin compactification of the space of configurations of n points on P 1 \{0, ∞} modulo scaling degenerates (isotrivially) to a compactification of the space of configurations of n points on A 1 modulo translation. The latter resembles the compactification constructed by Ziltener and Mau-Woodward, but allows the marked points to coincide, making it a G n−1 a -variety, which mirrors the fact that the Losev-Manin space is toric. The degeneration is compatible with the actions of G n−1 m and G n−1 a in the sense that these actions fit together globally in the total space of the degeneration.

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“…A remarkable compactification of the space of configurations of n distinct points on A 1 modulo translation is the moduli space Q n of 'stable scaled marked curves' constructed as a projective variety by Mau and Woodward in [MW10], after Ziltener discovered it in a symplectic setting [Zi06,Zi14]. The moduli space Q n plays an important role in the context of gauged stable maps [Wo15,GSW17,GSW18].…”

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confidence: 99%

Marked nodal curves with vector fields

Zahariuc¹

2021

Preprint

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We study 'bubbling up' on nodal curves in the style of Knudsen's proof that M g,n+1 is the universal curve over Mg,n, in the presence of a (logarithmic) vector field on the nodal curve. We propose a two-step bubbling up procedure. The first step is simply Knudsen stabilization with the additional data to keep track of. The second step ensures that the vector field doesn't vanish at the inserted point. These operations work in families.As an application, we prove that the Losev-Manin compactification of the space of configurations of n points on P 1 \{0, ∞} modulo scaling degenerates isotrivially to a compactification of the space of configurations of n points on A 1 modulo translation. The latter is related to the compactification constructed by Ziltener and Mau-Woodward, but allows the marked points to coincide, making it a G n−1 a -variety, which mirrors the fact that the Losev-Manin space is toric. Its combinatorics is dual to that of the space of phylogenetic trees of Billera-Holmes-Vogtmann. The degeneration is compatible with the actions of G n−1 m and G n−1 a in the sense that these actions fit together globally.

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Stable gauged maps

Cited by 3 publications

References 58 publications

Notes on coherent systems

Notes on coherent systems

Configurations of points on a line up to scaling or translation

Marked nodal curves with vector fields

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