Orbits in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math> and equivariant quantum cohomology

Lee, Mitchell; Patel, Anand; Spink, Hunter; Tseng, Dennis

doi:10.1016/j.aim.2019.106951

Advances in Mathematics

2020

DOI: 10.1016/j.aim.2019.106951

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Orbits in (Pr)n and equivariant quantum cohomology

Mitchell Lee¹,

Anand Patel²,

Hunter Spink³

et al.

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Cited by 4 publications

(1 citation statement)

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“…As noted by Lee-Patel-Spink-Tseng [LPST20], the proof of the second claim in Theorem 5.1 shows the weaker assertion that the formula in question is a lift of the class [Y π(v) ] T to A * G (A r×n ). However this lift may not, and generally does not, satisfy the degree bound of Theorem 3.5.…”

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confidence: 85%

Correction to: EQUIVARIANT CHOW CLASSES OF MATRIX VARIETIES

Berget

Fink

2021

Transformation Groups

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confidence: 85%

Correction to: EQUIVARIANT CHOW CLASSES OF MATRIX VARIETIES

Berget

Fink

2021

Transformation Groups

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Equivariant K-Theory Classes of Matrix Orbit Closures

Berget

Fink

2021

International Mathematics Research Notices

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The group $G = \textrm{GL}_r(k) \times (k^\times )^n$ acts on $\textbf{A}^{r \times n}$, the space of $r$-by-$n$ matrices: $\textrm{GL}_r(k)$ acts by row operations and $(k^\times )^n$ scales columns. A matrix orbit closure is the Zariski closure of a point orbit for this action. We prove that the class of such an orbit closure in $G$-equivariant $K$-theory of $\textbf{A}^{r \times n}$ is determined by the matroid of a generic point. We present two formulas for this class. The key to the proof is to show that matrix orbit closures have rational singularities.

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Orbits of Linear Series on the Projective Line

Deopurkar,

Patel

2024

International Mathematics Research Notices

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Orbits in (Pr)n and equivariant quantum cohomology

Cited by 4 publications

References 29 publications

Correction to: EQUIVARIANT CHOW CLASSES OF MATRIX VARIETIES

Correction to: EQUIVARIANT CHOW CLASSES OF MATRIX VARIETIES

Equivariant K-Theory Classes of Matrix Orbit Closures

Orbits of Linear Series on the Projective Line

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