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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hodge numbers of desingularized fiber products of elliptic surfaces
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by Chad Schoen;
Proc. Amer. Math. Soc. 152 (2024), 3215-3228
DOI: https://doi.org/10.1090/proc/16803
Published electronically: June 20, 2024

Abstract:

Each element of $(\Bbb Z_{\geq 0})^2$ is realized as the Hodge vector $(h^{3,0}(Z),h^{2,1}(Z))$ of some compact, connected, three dimensional, complex, submanifold, $Z\subset \Bbb P^N_{\Bbb C}$. Each $(x,y)\in (\Bbb Z_{\geq 1})^2$ with $y\leq 11x+8$ is shown to be the Hodge vector of a projective desingularized fiber product of elliptic surfaces which moves in moduli.
References
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Bibliographic Information
  • Chad Schoen
  • Affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708
  • MR Author ID: 156685
  • Email: schoen@math.duke.edu
  • Received by editor(s): December 10, 2022
  • Received by editor(s) in revised form: April 21, 2023, May 25, 2023, May 29, 2023, December 3, 2023, and January 31, 2024
  • Published electronically: June 20, 2024
  • Communicated by: Rachel Pries
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3215-3228
  • MSC (2020): Primary 14D07
  • DOI: https://doi.org/10.1090/proc/16803
  • MathSciNet review: 4767257