On Milnor classes via invariants of singular subschemes
James Fullwood
TL;DR
This paper presents a new formula relating the Milnor class of global complete intersections with the Segre class of their singular schemes, extending previous results to arbitrary singularities.
Contribution
It introduces a general formula for Milnor classes of complete intersections in smooth varieties, applicable to schemes with any singularities, generalizing Aluffi's hypersurface formula.
Findings
Derived a formula linking Milnor class and Segre class of singular schemes
Extended previous hypersurface results to arbitrary singularities
Provides a unified approach for computing Milnor classes in complex geometry
Abstract
We derive a formula for the Milnor class of scheme-theoretic global complete intersections (with arbitrary singularities) in a smooth variety in terms of the Segre class of its singular scheme. In codimension one the formula recovers a formula of Aluffi for the Milnor class of a hypersurface.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation