Identifier
etd-0515103-151156
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
Suppose $S$ is a parametrized surface in complex projective 3-space $mathbf{P}^3$ 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 Castelnuovo-Mumford 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.
Date
2003
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Wang, Haohao, "Equations of parametric surfaces with base points via syzygies" (2003). LSU Doctoral Dissertations. 3973.
https://repository.lsu.edu/gradschool_dissertations/3973
Committee Chair
William Adkins
DOI
10.31390/gradschool_dissertations.3973