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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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A vanishing theorem on fake projective planes with enough automorphisms
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by JongHae Keum PDF
Trans. Amer. Math. Soc. 369 (2017), 7067-7083 Request permission

Abstract:

For every fake projective plane $X$ with automorphism group of order 21, we prove that $H^i(X, 2L)=0$ for all $i$ and for every ample line bundle $L$ with $L^2=1$. For every fake projective plane with automorphism group of order 9, we prove the same vanishing for every cubic root (and its twist by a 2-torsion) of the canonical bundle $K$. As an immediate consequence, there are exceptional sequences of length 3 on such fake projective planes.
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Additional Information
  • JongHae Keum
  • Affiliation: School of Mathematics, Korea Institute for Advanced Study, Hoegiro 85, Dondaemungu, Seoul 02455, Korea
  • MR Author ID: 291447
  • Email: jhkeum@kias.re.kr
  • Received by editor(s): February 5, 2015
  • Received by editor(s) in revised form: October 20, 2015
  • Published electronically: March 29, 2017
  • Additional Notes: This research was supported by the National Research Foundation of Korea (NRF-2007-0093858)
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 7067-7083
  • MSC (2010): Primary 14J29, 14F05
  • DOI: https://doi.org/10.1090/tran/6856
  • MathSciNet review: 3683103