Characteristic classes in singularity theory PDF
Preview Characteristic classes in singularity theory
Thom polynomials of maps and bundle sections Characteristic classes in singularity theory Andrzej Weber joint with Malgorzata Mikosz and Piotr Pragacz AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials of maps and bundle sections Characteristic classes Thom polynomials in singularity theory Andrzej Weber joint with Malgorzata Mikosz and Piotr Pragacz AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials and bundle sections Characteristic classes Thom polynomials in singularity theory of maps Andrzej Weber joint with Malgorzata Mikosz and Piotr Pragacz AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials Characteristic classes Thom polynomials in singularity theory of maps and bundle sections Andrzej Weber joint with Malgorzata Mikosz and Piotr Pragacz AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials → Eg. vector field v on a manifold M P → Poincar´e–Hopf theorem: i (v) = χ(M) x ⇒ local contribution to a global invariant ⇐ non vanishing of the global invariant forces the existence of singularities Singularities Characteristic Classes ! Local Theory Global Theory AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials ⇒ local contribution to a global invariant ⇐ non vanishing of the global invariant forces the existence of singularities Singularities Characteristic Classes ! Local Theory Global Theory → Eg. vector field v on a manifold M P → Poincar´e–Hopf theorem: i (v) = χ(M) x AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials ⇐ non vanishing of the global invariant forces the existence of singularities Singularities Characteristic Classes ! Local Theory Global Theory → Eg. vector field v on a manifold M P → Poincar´e–Hopf theorem: i (v) = χ(M) x ⇒ local contribution to a global invariant AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials Singularities Characteristic Classes ! Local Theory Global Theory → Eg. vector field v on a manifold M P → Poincar´e–Hopf theorem: i (v) = χ(M) x ⇒ local contribution to a global invariant ⇐ non vanishing of the global invariant forces the existence of singularities AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials If c (ξ) 6= 0 then H 6= ∅ 1 Is H singular? Generically smooth (e.g. for ξ very ample) Singularities Σ ⊂ H have to occur in one-dimensional families ξ → M line bundle, s ∈ Γ(ξ) section H = {s = 0} hyperplane [H] = c (ξ) ∈ H2(M) 1 AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials Is H singular? Generically smooth (e.g. for ξ very ample) Singularities Σ ⊂ H have to occur in one-dimensional families ξ → M line bundle, s ∈ Γ(ξ) section H = {s = 0} hyperplane [H] = c (ξ) ∈ H2(M) 1 If c (ξ) 6= 0 then H 6= ∅ 1 AndrzejWeber Characteristicclassesinsingularitytheory:Thompolynomials
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