Integration on Artin toric stacks and Euler characteristics

Edidin, Dan; More, Yogesh

doi:10.1090/s0002-9939-2013-11849-6

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…In the case that ∆ is simplicial, one can generalize the degree map used in [12] to construct a correspondence between M W * (X(∆ )) and A * (X (∆ ) Q following [6].…”

Section: Conjectural Algorithm For the Image For Complete Toric Varietiesmentioning

confidence: 99%

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The vanishing of the chow cohomology ring for affine toric varieties and additional results

Richey¹

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From the recent work of Edidin and Satriano, given a good moduli space morphism between a smooth Artin stack and its good moduli space X, they prove that the Chow cohomology ring of X embeds into the Chow ring of the stack. In the context of toric varieties, this implies that the Chow cohomology ring of any toric variety embeds into the Chow ring of its canonical toric stack. Furthermore, the authors give a conjectural description of the image of this embedding in terms of strong cycles. One consequence of their conjectural description, and an additional conjecture, is that the Chow cohomology ring of any affine toric variety ought to vanish. We prove this result without any assumption on smoothness. Afterwards, we present a series of results related to their conjectural description, and finally, we provide a conjectural toric description of the image of this embedding for complete toric varieties by utilizing Minkowski weights.

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“…In the case that ∆ is simplicial, one can generalize the degree map used in [12] to construct a correspondence between M W * (X(∆ )) and A * (X (∆ ) Q following [6].…”

Section: Conjectural Algorithm For the Image For Complete Toric Varietiesmentioning

confidence: 99%

“…the remaining examples, their resolutions are merely simplicial, and hence, this may affect their results even though we are utilizing the method of [6] to generalize the degree map.…”

Section: Output Of the Algorithmmentioning

confidence: 99%

The vanishing of the chow cohomology ring for affine toric varieties and additional results

Richey¹

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Towards an Intersection Chow Cohomology Theory for Git Quotients

Edidin

Satriano

2020

Transformation Groups

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We study the Fulton-MacPherson operational Chow rings of good moduli spaces of properly stable, smooth, Artin stacks. Such spaces areétale locally isomorphic to geometric invariant theory quotients of affine schemes, and are therefore natural extensions of GIT quotients. Our main result is that, with Q-coefficients, every operational class can be represented by a topologically strong cycle on the corresponding stack. Moreover, this cycle is unique modulo rational equivalence on the stack. Our methods also allow us to prove that if X is the good moduli space of a properly stable, smooth, Artin stack then the natural map Pic(X) Q → A 1 op (X) Q , L → c1(L) is an isomorphism.

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Toric Sheaves on Hirzebruch Orbifolds

Wang

2020

Doc. Math.

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We provide a stacky fan description of the total space of certain split vector bundles, as well as their projectivization, over toric Deligne-Mumford stacks. We then specialize to the case of Hirzebruch orbifolds H ab r obtained by projectivizing O ⊕ O(r) over the weighted projective line P(a, b). Next, we give a combinatorial description of toric sheaves on H ab r and investigate their basic properties. With fixed choice of polarization and a generating sheaf, we describe the fixed point locus of the moduli scheme of µ-stable torsion free sheaves of rank 1 and 2 on H ab r . As an example, we obtain explicit formulas for generating functions of Euler characteristics of locally free sheaves of rank 2 on P(1, 2) × P 1 .

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Integration on Artin toric stacks and Euler characteristics

Cited by 3 publications

References 11 publications

The vanishing of the chow cohomology ring for affine toric varieties and additional results

The vanishing of the chow cohomology ring for affine toric varieties and additional results

Towards an Intersection Chow Cohomology Theory for Git Quotients

Toric Sheaves on Hirzebruch Orbifolds

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