Type of Document Dissertation Author Tzigantchev, Dimitre Gueorguiev Author's Email Address firstname.lastname@example.org URN etd-11012006-162123 Title Predegree Polynomials of Plane Configurations in Projective Space Degree Doctor of Philosophy Department Mathematics, Department of Advisory Committee
Advisor Name Title Paolo Aluffi Committee Chair Eric Klassen Committee Member Ettore Aldrovandi Committee Member Laura Reina Committee Member Mika Seppala Committee Member Keywords
Date of Defense 2006-10-30 Availability unrestricted AbstractWe work over an algebraically closed ground field of characteristic zero. The group
of PGL(4) acts naturally on the projective space P^N parameterizing surfaces of a given
degree d in P^3. The orbit of a surface under this action is the image of a rational map from P^15 to P^N. The closure of the orbit is a natural and interesting object to study.
Its predegree is defined as the degree of the orbit closure multiplied by the degree of the above
map restricted to a general P^j , j being the dimension of the orbit. We find the predegrees
and other invariants for all surfaces supported on unions of planes. The information is
encoded in the so-called adjusted predegree polynomials, which possess nice multiplicative
properties allowing us to easily compute the predegree (polynomials) of various special plane
The predegree has both a combinatorial and geometric significance. The results obtained
in this thesis would be a necessary step in the solution of the problem of computing predegrees
for all surfaces.
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