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F4 and desmic quartic surfaces
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DOI：10.1007/s10455-026-10028-5.png)
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Abstract
En 中文
The desmic pencil of quartic surfaces is part of a beautiful, but mostly forgotten chapter of the classical theory of algebraic surfaces: it is the only non-degenerate pencil of quartic surfaces in P-3 containing at least three completely reducible members. We observe in this note that it is closely related to the Weyl group of the root system F-4, and can be recovered from a series of symmetric spaces deduced from the exceptional Lie algebras. We discuss the main properties of the pencil from this Lie theoretic point of view.
Keywords:
Kummer surface
Quartic surface
Desmic pencil
Hesse pencil
Little Weyl group
Exceptional Lie group
Journal
A
IF:
0.7
Papers:
29
Citations:
0