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Chern Classes of Sheaves of Logarithmic Vector Fields for Free Divisors

Title: Chern Classes of Sheaves of Logarithmic Vector Fields for Free Divisors.
Name(s): Liao, Xia, author
Aluffi, Paolo, professor directing dissertation
Reina, Laura, university representative
Klassen, Eric P., committee member
Aldrovandi, Ettore, committee member
Petersen, Kathleen, committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2013
Publisher: Florida State University
Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: The thesis work we present here focuses on solving a conjecture raised by Aluffi about Chern-Schwartz-MacPherson classes. Let $X$ be a nonsingular variety defined over an algebraically closed field $k$ of characteristic $0$, $D$ a reduced effective divisor on $X$, and $U = X smallsetminus D$ the open complement of $D$ in $X$. The conjecture states that $c_{textup{SM}}(1_U) = c(textup{Der}_X(-log D)) cap [X]$ in $A_{*}(X)$ for any locally quasi-homogeneous free divisor $D$. We prove a stronger version of this conjecture. We also report on work aimed at studying the Grothedieck class of hypersurfaces of low degree. In this work, we verified the Geometric Chevalley-Warning conjecture in several low dimensional cases.
Identifier: FSU_migr_etd-7467 (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: Summer Semester, 2013.
Date of Defense: May 17, 2013.
Bibliography Note: Includes bibliographical references.
Advisory Committee: Paolo Aluffi, Professor Directing Dissertation; Laura Reina, University Representative; Eric P. Klassen, Committee Member; Ettore Aldrovandi, Committee Member; Kathleen Petersen, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record:
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Host Institution: FSU

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Liao, X. (2013). Chern Classes of Sheaves of Logarithmic Vector Fields for Free Divisors. Retrieved from