Rees algebras and iterated Jacobian duals

<p>Consider the rational map Ψ : [Special characters omitted.] where the <em>fi</em>'s are homogeneous forms of the same degree in the homogeneous coordinate ring <em>R</em> = <em>k</em>[<em> x</em>1,…,<em>xd</em>] of [Special characters omitted.]. Assume that <em>I</em> = (<em>f</em> 1,…,<em>fm</em>) is a height 2 perfect ideal in the polynomial ring <em>R.</em> In this context, the coordinate ring of the graph of Ψ is the Rees algebra of <em>I</em> and the co-ordinate ring of the image of Ψ is the special fiber ring. We study two settings. The first setting is when <em>I</em> is almost linearly presented. Here we study the ideal defining the graph and the image of Ψ. Whenever possible, we also study invariants such as the Castelnuovo-Mumford regularity and the relation type of the graph of Ψ. In the second setting we impose no constraints on the column degrees of the presentation matrix of <em>I</em>, but the number of generators of <em>I</em> is restricted to <em>d</em> + 1 (two more than the dimension of the source of Ψ). For this configuration, we study the image of Ψ.</p> <p>We also introduce a new method, namely "iterated'' Jacobian duals, to study the graph of Ψ. This is a generalization of the usual Jacobian duals which are often used to describe the graph of Ψ.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2016

Author dc:creator

• Mukundan, Vivek

Contributors dc:contributor

• Bernd Ulrich
• Giulio Caviglia
• Edray H. Goins
• William J. Heinzer

• Pure sciences
• Almost linearly presented ideals
• Blowup algebras
• Image of rational map
• Iterated Jacobian duals
• Rees algebras
• Second analytic deviation one ideals
• Mathematics

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/818

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-2010