This project supports research in commutative algebra and algebraic geometry. The principal investigators will study torsion-free, projective and Cohen-Macaulay modules over affine rings and their localizations; prime ideal structure of two-dimensional affine domains; and Hilbert functions and reduction numbers of primary ideals in Cohen-Macaulay local rings. They will also consider automorphism groups of rational surfaces; ideal theoretic questions of embedded rational surfaces; and the set-theoretic complete intersection problem for curves in projective 3-space. Algebraic geometry is the study of the geometric objects arising from the sets of zeros of systems of polynomial equations. This is one of the oldest and currently one of the most active branches of mathematics. It has widespread applications in mathematics, computer science and physics.
