Characteristic classes of complex hypersurfaces |
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Authors: | Sylvain E Cappell Jörg Schürmann |
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Institution: | a Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA b Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706-1388, USA c Mathematische Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany d Department of Mathematics, University of Pennsylvania, 209 S 33rd St., Philadelphia, PA 19104, USA |
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Abstract: | The Milnor-Hirzebruch class of a locally complete intersection X in an algebraic manifold M measures the difference between the (Poincaré dual of the) Hirzebruch class of the virtual tangent bundle of X and, respectively, the Brasselet-Schürmann-Yokura (homology) Hirzebruch class of X. In this note, we calculate the Milnor-Hirzebruch class of a globally defined algebraic hypersurface X in terms of the corresponding Hirzebruch invariants of vanishing cycles and singular strata in a Whitney stratification of X. Our approach is based on Schürmann's specialization property for the motivic Hirzebruch class transformation of Brasselet-Schürmann-Yokura. The present results also yield calculations of Todd, Chern and L-type characteristic classes of hypersurfaces. |
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Keywords: | 32S20 14B05 14J17 32S25 32S35 32S40 32S50 32S60 14C17 14C30 14J70 32S30 32S55 58K10 |
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