Lines in supersingular quartics
Date
2021-10-19
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Source Title
Mathematical Society of Japan. Journal
Print ISSN
0025-5645
Electronic ISSN
1881-1167
Publisher
Nihon Sugakkai,Mathematical Society of Japan
Volume
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Pages
1 - 47
Language
English
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Abstract
We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the number of lines is at most 60 in both cases. We also give a complete classification of large configurations of lines.