Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Curve counting invariants for crepant resolutions
HTML articles powered by AMS MathViewer

by Jim Bryan and David Steinberg PDF
Trans. Amer. Math. Soc. 368 (2016), 1583-1619 Request permission

Abstract:

We construct curve counting invariants for a Calabi-Yau threefold $Y$ equipped with a dominant birational morphism $\pi :Y \to X$. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when $\pi :Y\to Y$ is the identity. Our main result is a PT/DT-type formula relating the partition function of our invariants to the Donaldson-Thomas partition function in the case when $Y$ is a crepant resolution of $X$, the coarse space of a Calabi-Yau orbifold $\mathcal {X}$ satisfying the hard Lefschetz condition. In this case, our partition function is equal to the Pandharipande-Thomas partition function of the orbifold $\mathcal {X}$. Our methods include defining a new notion of stability for sheaves which depends on the morphism $\pi$. Our notion generalizes slope stability which is recovered in the case where $\pi$ is the identity on $Y$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14N35
  • Retrieve articles in all journals with MSC (2010): 14N35
Additional Information
  • Jim Bryan
  • Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
  • ORCID: 0000-0003-2541-5678
  • Email: jbryan@math.ubc.ca
  • David Steinberg
  • Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
  • Address at time of publication: Department of Mathematics, Fenton Hall, University of Oregon, Eugene, Oregon 97403-1222
  • Email: dsteinbe@math.ubc.ca, dcstein@uoregon.edu
  • Received by editor(s): August 20, 2012
  • Received by editor(s) in revised form: December 18, 2013
  • Published electronically: June 15, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 1583-1619
  • MSC (2010): Primary 14N35
  • DOI: https://doi.org/10.1090/tran/6377
  • MathSciNet review: 3449219