Type of Document	Dissertation
Author	Tzigantchev, Dimitre Gueorguiev
Author's Email Address	dtzigant@math.fsu.edu
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	Arrangements Hyperplane Line
Date of Defense	2006-10-30
Availability	unrestricted
Abstract We 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 configurations. 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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