Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022
Nobuhiro Honda ^{[a]} and Ayato Minagawa ^{[a,b]}
On the cuspidal locus in the dual varieties of Segre quartic surfaces
Pages: 551610
Received: 16 December 2021
Accepted: 27 July 2022
Mathematics Subject Classification: 53C26, 14D06.
Keywords: Segre surfaces, cuspidal curves, projectively dual varieties, minitwistor spaces.
Authors address:
[a]: Tokyo Institute of Technology, Department of Mathematics, Meguro, Japan
[b]: Internet Initiative Japan Inc.
The first author was partially supported by JSPS KAKENHI Grant 16H03932
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Abstract:
Motivated by a kind of Penrose correspondence, we investigate
the space of hyperplane sections of Segre quartic surfaces which
have an ordinary cusp. We show that the space of such hyperplane sections
is empty for two kinds of Segre surfaces, and it is a connected
surface for all other kinds of Segre surfaces. We also show that when it
is nonempty, the closure of the space is either birational to the surface
itself or birational to a double covering of the surface, whose branch divisor
consists of some specific lines on the surface.
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