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Characteristic Classes and Local Invariants of Determinantal Varieties and a Formula for Equivariant Chern-Schwartz-MacPherson Classes of Hypersurfaces

Title: Characteristic Classes and Local Invariants of Determinantal Varieties and a Formula for Equivariant Chern-Schwartz-MacPherson Classes of Hypersurfaces.
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Name(s): Zhang, Xiping, author
Aluffi, Paolo, 1960-, professor directing dissertation
Piekarewicz, Jorge, university representative
Aldrovandi, Ettore, committee member
Petersen, Kathleen L., committee member
Hoeij, Mark van, committee member
Florida State University, degree granting institution
College of Arts and Sciences, degree granting college
Department of Mathematics, degree granting department
Type of Resource: text
Genre: Text
Master Thesis
Issuance: monographic
Date Issued: 2018
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (106 pages)
Language(s): English
Abstract/Description: Determinantal varieties parametrize spaces of matrices of given ranks. The main results of this dissertation are computations of intersection-theoretic invariants of determinantal varieties. We focus on the Chern-Mather and Chern-Schwartz-MacPherson classes, on the characteristic cycles, and on topologically motivated invariants such as the local Euler obstruction. We obtain explicit formulas in both the ordinary and the torus-equivariant setting, and formulate a conjecture concerning the effectiveness of the Chern-Schwartz-MacPherson classes of determinantal varieties. We also prove a vanishing property for the Chern-Schwartz-MacPherson classes of general group orbits. As applications we obtain formulas for the sectional Euler characteristic of determinantal varieties and the microlocal indices of their intersection cohomology sheaf complexes. Moreover, for a close embedding we define the equivariant version of the Segre class and prove an equivariant formula for the Chern-Schwartz-MacPherson classes of hypersurfaces of projective varieties.
Identifier: 2018_Sp_Zhang_fsu_0071N_14521 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Spring Semester 2018.
Date of Defense: April 11, 2018.
Keywords: Chern classes, determinantal variety, equivariant Chern classes, local Euler obstruction
Bibliography Note: Includes bibliographical references.
Advisory Committee: Paolo Aluffi, Professor Directing Dissertation; Jorge Piekarewicz, University Representative; Ettore Aldrovandi, Committee Member; Kate Petersen, Committee Member; Mark van Hoeij, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/2018_Sp_Zhang_fsu_0071N_14521
Host Institution: FSU

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Zhang, X. (2018). Characteristic Classes and Local Invariants of Determinantal Varieties and a Formula for Equivariant Chern-Schwartz-MacPherson Classes of Hypersurfaces. Retrieved from http://purl.flvc.org/fsu/fd/2018_Sp_Zhang_fsu_0071N_14521