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Generators of fat point ideals on the projective plane
Abstract
This work employs geometric methods to investigate the relationship between the geometry of fat point subschemes of the projective plane and the structure of their defining ideals. In particular, for fat point subschemes supported at any six general points of the projective plane, we determine the number of elements of each degree in a minimal set of homogeneous generators for the defining ideal, called a fat point ideal. This, in turn, implicitly determines a minimal free resolution of the ideal. For fat point ideals whose zero locus is a set of seven or eight points in general position, for every degree but one we determine the number of elements in a minimal set of homogeneous generators. Under some additional technical hypotheses which ensure our ability to do necessary computations, for every degree but one we determine bounds on the number of elements in a minimal set of homogeneous generators for fat point ideals with a zero locus of more than eight points. Finally, we compare the bounds we obtain with previously known bounds due to Campanella.
Subject Area
Mathematics
Recommended Citation
Fitchett, Stephanie Ann, "Generators of fat point ideals on the projective plane" (1997). ETD collection for University of Nebraska-Lincoln. AAI9734617.
https://digitalcommons.unl.edu/dissertations/AAI9734617