Scholarlink

<p>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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathbb {P}}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(F_4\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation>, 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

\(F_4\) and desmic quartic surfaces

  • 期刊论文

  • 发表日期：

    2026年2月2日

查看全文
  • Laurent Manivel

摘要

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 \({\mathbb {P}}^3\) 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 \(F_4\) 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.