AbstractsMathematics
| Institution: | The Ohio State University |
|---|---|
| Department: | Mathematics |
| Degree: | PhD |
| Year: | 2010 |
| Keywords: | Mathematics; gradient ideal; symmetric obstruction theory; Hodge locus; multi-gradient ideal |
| Record ID: | 1880718 |
| Full text PDF: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1280803107 |
Abstract
The notion of gradient ideals in a power series algebra over a noetherian local ring is defined with basic properties studied. A natural generalization, “multi-gradient ideals”, and the algebra of potential functions associated to an arbitrary ideal are introduced. Classification of multi-gradient ideals is given in the cases of principal ideals and monomial ideals by studying their algebras of potential functions. Abstract examples of non-multi-gradient ideals and geometric examples of multi-gradient ideals are constructed.
