Cohomological and K-theoretic invariants of singularity loci

Diplôme Thèse Cohomological and K-theoretic invariants of singularity loci eng 2018-08-06 author Kolokolnikova Natalia 751023 director Szenes Andras 664272 10.13097/archive-ouverte/unige:107242 urn:nbn:ch:unige-1072428 Sc. 5244 This thesis is devoted to the study of singularities of holomorphic maps: their geometry, as well as cohomological and K-theoretic invariants, their properties and computational strategies. One of the main problems in global singularity theory is how to compute Thom polynomials. I show how the two modern methods of computation can be combined in a different computational approach and give examples of computation. A recent development in global singularity theory is the introduction of the K-theoretic invariants of singularity loci. One can define a K-theoretic invariant of an affine variety in two different ways. I prove that even for A2 singularity loci, in the general case, the two invariants are different, and therefore, the A2-loci may have singularities worse than rational. However, in the case of relative codimension 0, the two invariants coincide, and thus the A2-loci have rational singularities. Singularity Thom polynomial K-theory Dewey 510 25 Section de mathématiques 11 false 99d7317d-da91-4852-947d-a0e1fc438b46 Thesis Public telegram-cloud-document-2-5465243380470514275--5968714813981370546.pdf 856049 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Cohomological and K-theoretic invariants of singularity loci				2018	831	696

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Kolokolnikova, Natalia