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<p>Brasselet, the second author and Yokura introduced Hodge-theoretic Hirzebruch-type characteristic classes <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(IT_{1, *}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>I</mi> <msub> <mi>T</mi> <mrow> <mn>1</mn> <mo>,</mo> <mrow /> <mo>∗</mo> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>, and conjectured that they are equal to the Goresky-MacPherson <i>L</i>-classes for pure-dimensional compact complex algebraic varieties. In this paper, we show that the framework of Gysin coherent characteristic classes of singular complex algebraic varieties developed by the first and third author in previous work applies to the characteristic classes <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(IT_{1, *}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>I</mi> <msub> <mi>T</mi> <mrow> <mn>1</mn> <mo>,</mo> <mrow /> <mo>∗</mo> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>. In doing so, we prove the ambient version of the above conjecture for subvarieties in a Grassmannian. Since the homology of Schubert subvarieties injects into the homology of the ambient Grassmannian, this implies the conjecture for all Schubert varieties in a Grassmannian. We also study other algebraic characteristic classes such as Chern classes and Todd classes (or their variants for the intersection cohomology sheaves) within the framework of Gysin coherent characteristic classes.</p>

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Topological Gysin Coherence for Algebraic Characteristic Classes of Singular Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月2日

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  • Markus Banagl,
  • Jörg Schürmann,
  • Dominik J. Wrazidlo

摘要

Brasselet, the second author and Yokura introduced Hodge-theoretic Hirzebruch-type characteristic classes \(IT_{1, *}\) I T 1 , ∗ , and conjectured that they are equal to the Goresky-MacPherson L-classes for pure-dimensional compact complex algebraic varieties. In this paper, we show that the framework of Gysin coherent characteristic classes of singular complex algebraic varieties developed by the first and third author in previous work applies to the characteristic classes \(IT_{1, *}\) I T 1 , ∗ . In doing so, we prove the ambient version of the above conjecture for subvarieties in a Grassmannian. Since the homology of Schubert subvarieties injects into the homology of the ambient Grassmannian, this implies the conjecture for all Schubert varieties in a Grassmannian. We also study other algebraic characteristic classes such as Chern classes and Todd classes (or their variants for the intersection cohomology sheaves) within the framework of Gysin coherent characteristic classes.