Mathematical Sciences: Linkage, Symmetric Algebras, and Hyperplane Sections

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This award supports research in three areas of commutative algebra. The first part of this work is directed at studying linkage. The principal investigator will study a numerical condition on the graded resolution that might imply that an ideal is licci. He also will study the relation between several possible definitions for a local ring to be licci. The second part of his work is concerned with symmetric algebras of modules and Vasconcelos' Factorial Conjecture. The third part of his work is aimed at understanding reduced and irreducible projective curves in terms of their general hyperplane sections. This is reasearch in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origins, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in theoretical computer science and robotics.