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<p>Let <i>Y</i> be a smooth cubic fourfold not containing any plane, <i>F</i> be its Fano variety of lines and <i>Z</i> be its associated LLSvS variety, parametrizing families of twisted cubics and some of their degenerations. In this short note, we show that for the general cubic fourfold the divisor of singular cubic surfaces on <i>Z</i> has two irreducible components, one of which coincides with the uniruled branch divisor of a resolution of the Voisin map <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F\times F \dashrightarrow Z\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>×</mo> <mi>F</mi> <mo>⤏</mo> <mi>Z</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On the uniruled Voisin divisor on the LLSvS variety

  • 期刊论文

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  • 发表日期：

    2026年5月6日

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  • Franco Giovenzana

摘要

Let Y be a smooth cubic fourfold not containing any plane, F be its Fano variety of lines and Z be its associated LLSvS variety, parametrizing families of twisted cubics and some of their degenerations. In this short note, we show that for the general cubic fourfold the divisor of singular cubic surfaces on Z has two irreducible components, one of which coincides with the uniruled branch divisor of a resolution of the Voisin map \(F\times F \dashrightarrow Z\) F × F ⤏ Z .