
Type of Document Dissertation Author Wang, Haohao Author's Email Address hwang4@lsu.edu URN etd0515103151156 Title Equations of Parametric Surfaces with Base Points via Syzygies Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title William Adkins Committee Chair Augusto Nobile Committee Member Frank Neubrander Committee Member Jerome Hoffman Committee Member Jimmie Lawson Committee Member Leszek Czarnecki Dean's Representative Keywords
 saturation
 regularity
 syzygy
 base point
 implicitization
 biprojective space
Date of Defense 20030506 Availability unrestricted Abstract Suppose $S$ is a parametrized surface in complex projective3space $mathbf{P}^3$ given as the image of $phi: mathbf{P}^1
imes mathbf{P}^1 o mathbf{P}^3$. The implicitization problem
is to compute an implicit equation $F=0$ of $S$ using the
parametrization $phi$. An algorithm using syzygies exists for
computing $F$ if $phi$ has no base points, i.e. $phi$ is
everywhere defined. This work is an extension of this algorithm to
the case of a surface with multiple base points of total
multiplicity k.
We accomplish this in three chapters. In Chapter 2, we develop
the concept and properties of CastelnuovoMumford regularity in
biprojective spaces. In Chapter 3, we give a criterion for
regularity in biprojective spaces. These results are applied to the
implicitization problem in Chapter 4.
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