 

Nobuhiro Honda
Segre quartic surfaces and minitwistor spaces
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Published: 
April 1, 2022. 
Keywords: 
minitwistor space, EinsteinWeyl structure, nodal rational curve, Segre surface. 
Subject: 
53C26, 14D06. 


Abstract
The Segre surfaces of the title are by definition those quartic surfaces in CP_{4}
that arise as images of weak del Pezzo surfaces of degree four under the anticanonical map.
We first show that under some minimality condition, minitwistor spaces of genus one
are exactly Segre quartic surfaces. By a kind of Penrose correspondence,
Zariski open subsets of the projective dual varieties of these surfaces
admit EinsteinWeyl structure. We investigate structures of these dual varieties in detail.
In particular, we determine the degrees of these varieties (namely the classes of the Segre surfaces),
as well as structure of several components of the divisors at infinity,
which are the complements of the EinsteinWeyl spaces in the projective dual varieties.


Acknowledgements
The author has been partially supported by JSPS KAKENHI Grant 16H03932.


Author information
Nobuhiro Honda:
Department of Mathematics
Tokyo Institute of Technology, Japan
honda@math.titech.ac.jp

