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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Equivariant Chow cohomology of nonsimplicial toric varieties
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by Hal Schenck PDF
Trans. Amer. Math. Soc. 364 (2012), 4041-4051 Request permission


For a toric variety $X_\Sigma$ determined by a polyhedral fan $\Sigma \subseteq N$, Payne shows that the equivariant Chow cohomology is the $\mathrm {Sym}(N)$-algebra $C^0(\Sigma )$ of integral piecewise polynomial functions on $\Sigma$. We use the Cartan-Eilenberg spectral sequence to analyze the associated reflexive sheaf $\mathcal {C}^0(\Sigma )$ on $\mathbb {P}_{\mathbb {Q}}(N)$, showing that the Chern classes depend on subtle geometry of $\Sigma$ and giving criteria for the splitting of $\mathcal {C}^0(\Sigma )$ as a sum of line bundles. For certain fans associated to the reflection arrangement $\mathrm {A_n}$, we describe a connection between $C^0(\Sigma )$ and logarithmic vector fields tangent to $\mathrm {A_n}$.
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Additional Information
  • Hal Schenck
  • Affiliation: Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801
  • MR Author ID: 621581
  • Email:
  • Received by editor(s): March 1, 2010
  • Received by editor(s) in revised form: June 29, 2010
  • Published electronically: February 17, 2012
  • Additional Notes: The author was supported by NSF 0707667
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 4041-4051
  • MSC (2010): Primary 14M25; Secondary 14F43, 13D02, 52B99
  • DOI:
  • MathSciNet review: 2912444