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SMOOTHNESS IN PENCILS OF HYPERSURFACES OVER FINITE FIELDS

Part of: Projective and enumerative geometry Arithmetic problems. Diophantine geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  25 August 2022

SHAMIL ASGARLI Open the ORCID record for SHAMIL ASGARLI [Opens in a new window]  and
DRAGOS GHIOCA Open the ORCID record for DRAGOS GHIOCA [Opens in a new window]
SHAMIL ASGARLI
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada e-mail: [email protected]
DRAGOS GHIOCA*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
*
e-mail: [email protected]
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Abstract

We study pencils of hypersurfaces over finite fields $\mathbb {F}_q$ such that each of the $q+1$ members defined over $\mathbb {F}_q$ is smooth.

Keywords

pencils of hypersurfacesfinite fieldssmoothness

MSC classification

Primary: 14N05: Projective techniques
Secondary: 14G15: Finite ground fields 14J70: Hypersurfaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 1 , February 2023 , pp. 85 - 94
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is supported by a Postdoctoral Research Fellowship and an NSERC PDF award at the University of British Columbia. The second author is supported by an NSERC Discovery grant.

References

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