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DYNAMICAL SYSTEMS ON SOME ELLIPTIC MODULAR SURFACES VIA OPERATORS ON LINE ARRANGEMENTS
- Part of
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- Journal:
- Nagoya Mathematical Journal , First View
- Published online by Cambridge University Press:
- 20 January 2025, pp. 1-19
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- Article
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This paper further studies the matroid realization space of a specific deformation of the regular n-gon with its lines of symmetry. Recently, we obtained that these particular realization spaces are birational to the elliptic modular surfaces
$\Xi _{1}(n)$ over the modular curve 
$X_1(n)$. Here, we focus on the peculiar cases when 
$n=7,8$ in more detail. We obtain concrete quartic surfaces in 
$\mathbb {P}^3$ equipped with a dominant rational self-map stemming from an operator on line arrangements, which yields K3 surfaces with a dynamical system that is semi-conjugated to the plane.
