Lines on K3 quartic surfaces in characteristic 3
Keyword(s):
AbstractWe investigate the number of straight lines contained in a K3 quartic surface X defined over an algebraically closed field of characteristic 3. We prove that if X contains 112 lines, then X is projectively equivalent to the Fermat quartic surface; otherwise, X contains at most 67 lines. We improve this bound to 58 if X contains a star (ie four distinct lines intersecting at a smooth point of X). Explicit equations of three 1-dimensional families of smooth quartic surfaces with 58 lines, and of a quartic surface with 8 singular points and 48 lines are provided.
2018 ◽
Vol 70
(5)
◽
pp. 1038-1075
◽
2017 ◽
Vol 16
(01)
◽
pp. 1750012
2000 ◽
Vol 128
(3)
◽
pp. 395-423
◽
Keyword(s):
Keyword(s):
1959 ◽
Vol 14
◽
pp. 223-234
◽
Keyword(s):
2013 ◽
Vol 89
(2)
◽
pp. 234-242
◽
2014 ◽
Vol 35
(7)
◽
pp. 2242-2268
◽
2011 ◽
Vol 11
(2)
◽
pp. 221-271
◽
1976 ◽
Vol 59
(1)
◽
pp. 29-29
◽
Keyword(s):