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Intersection homology and Alexander modules of hypersurface complements
Let $V$ be a degree $d$, reduced hypersurface in $\mathbb{CP}^{n+1}$, $n \geq 1$, and fix a generic hyperplane, $H$. Denote by $\mathcal{U}$ the (affine) hypersurface complement, $\mathbb{CP}^{n+1}-V
Characteristic classes of complex hypersurfaces
Abstract The Milnor–Hirzebruch class of a locally complete intersection X in an algebraic manifold M measures the difference between the (Poincare dual of the) Hirzebruch class of the virtual tangent
Twisted genera of symmetric products
We give a new proof of formulae for the generating series of (Hodge) genera of symmetric products X(n) with coefficients, which hold for complex quasi-projective varieties X with any kind of
A decomposition theorem for the peripheral complex associatedwith hypersurfaces
We give necessary and sufficient conditions for a decomposition (in the category of perverse sheaves) of the Cappell-Shaneson peripheral complex associated with a complex affine hypersurface. We also
Intersection cohomology invariants of complex algebraic varieties
In this note we use the deep BBDG decomposition theorem in order to give a new proof of the so-called "stratified multiplicative property" for certain intersection cohomology invariants of complex
Perverse Sheaves
  • L. Maxim
  • Graduate Texts in Mathematics
  • 2019
Intersection Homology & Perverse Sheaves
  • L. Maxim
  • Mathematics
    Graduate Texts in Mathematics
  • 1 December 2019
Multivariable alexander invariants of hypersurface complements
We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin's
Deformation of Singularities and the Homology of Intersection Spaces
While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic
Characteristic classes of symmetric products of complex quasi-projective varieties
We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch