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1. Liu, Yu-Han. Gradient ideals.

Degree: PhD, Mathematics, 2010, The Ohio State University

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. Advisors/Committee Members: Clemens, Herbert (Advisor).

Subjects/Keywords: Mathematics; gradient ideal; symmetric obstruction theory; Hodge locus; multi-gradient ideal

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APA (6th Edition):

Liu, Y. (2010). Gradient ideals. (Doctoral Dissertation). The Ohio State University. Retrieved from

Chicago Manual of Style (16th Edition):

Liu, Yu-Han. “Gradient ideals.” 2010. Doctoral Dissertation, The Ohio State University. Accessed July 10, 2020.

MLA Handbook (7th Edition):

Liu, Yu-Han. “Gradient ideals.” 2010. Web. 10 Jul 2020.


Liu Y. Gradient ideals. [Internet] [Doctoral dissertation]. The Ohio State University; 2010. [cited 2020 Jul 10]. Available from:

Council of Science Editors:

Liu Y. Gradient ideals. [Doctoral Dissertation]. The Ohio State University; 2010. Available from: