The Library
Free divisors and their deformations
Tools
Torielli, Michele (2012) Free divisors and their deformations. PhD thesis, University of Warwick.
|
Text
WRAP_THESIS_Torielli_2012.pdf - Submitted Version Download (717Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2604425~S1
Abstract
A reduced divisor D = V (f) Cn is free if the sheaf Der(-logD) := f 2
DerCn (f) 2 (f)OCng of logarithmic vector fields is a locally free OCn-module.
It is linear if, furthermore, Der(-logD) is globally generated by a basis consisting
of vector fields all of whose coefficients, with respect to the standard basis
@=@x1;...; @=@xn of the space DerCn of vector fields on Cn, are linear functions.
In principle, linear free divisors, like other kinds of singularities, might be expected
to appear in non-trivial parameterised families. As part of this thesis, however, we
prove that for reductive linear free divisors, there are no formally non-trivial families,
where a linear free divisor is reductive if its associated Lie algebra is reductive, thus
reductive linear free divisors are formally rigid.
To prove this and to understand better the class of free divisors, we introduce a
rigorous deformation theory for germs of free and linear free divisors. A (linearly)
admissible deformation is a deformation in which we deform a germ of a (linear) free
divisor (D; 0) c (Cn; 0) in such a way that each fiber of the deformation is still a
(linear) free divisor and that the singular locus of (D; 0) is deformed
atly. Moreover,
we explain how to use the de Rham logarithmic complex to compute the space of first
order infinitesimal admissible deformations and the Lie algebra cohomology complex
to compute the space of first order infinitesimal linearly admissible deformations.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Divisor theory, Deformations of singularities | ||||
Official Date: | June 2012 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Mond, D. (David) | ||||
Extent: | v, 136 leaves | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year