Connections Between Algebra, Combinatorics, and Geometry [Paperback]

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 23, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Preface.- Differential Graded Commutative Algebra.- Secant Varieties.- Fat Points and Symbolic Powers.- An Introduction to Stanley-Reisner Rings.- Combinatorial Resolutions.- Geometric Properties of the Tor Algebra Structure for Trivariate Monomial Ideals.- Interactions Between Linear Algebra and Algebraic Geometry.- Fat Points.- Primary Decomposition of Certain Permanental Ideals.Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics,?and Geometry contains lecture notes, along with exercises and?solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It all3¬