Details

Nobuhiro Honda ^[a] and Ayato Minagawa ^[a,b]

On the cuspidal locus in the dual varieties of Segre quartic surfaces

Pages: 551-610
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.

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 non-empty, 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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