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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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Morse theory and toric vector bundles
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by David Treumann PDF
Trans. Amer. Math. Soc. 369 (2017), 1-29 Request permission

Abstract:

Morelli’s computation of the $K$-theory of a toric variety $X$ associates a polyhedrally constructible function on a real vector space to every equivariant vector bundle $\mathcal {E}$ on $X$. The coherent-constructible correspondence lifts Morelli’s constructible function to a complex of constructible sheaves $\kappa (\mathcal {E})$. We show that certain filtrations of the cohomology of $\kappa (\mathcal {E})$ coming from Morse theory coincide with the Klyachko filtrations of the generic stalk of $\mathcal {E}$. We give Morse-theoretic (i.e. microlocal) conditions for a complex of constructible sheaves to correspond to a vector bundle and to a nef vector bundle.
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Additional Information
  • David Treumann
  • Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467-3806
  • Received by editor(s): August 21, 2012
  • Received by editor(s) in revised form: December 27, 2013, June 25, 2014, and July 12, 2014
  • Published electronically: August 22, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1-29
  • MSC (2010): Primary 14M25
  • DOI: https://doi.org/10.1090/tran/6511
  • MathSciNet review: 3557766