On Hilbert Functions and H-Vectors of Graded Modules

In this research, we study the Hilbert functions and h-vectors of graded modules with support on finite sets of points in projective space. To attain this, we construct the graded modules from the sets of points in projective space. We use a computer software package for algebraic computations Macaulay 2 to study the behavior of the Hilbert functions, h-vectors and Betti diagrams of the constructed graded modules. This book is divided into 6 chapters, the main results have been discussed in chapters 3, 4 and 5.

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BSc. with Education (Mathematics and Informatics), MSc (Mathematics), teaches at the Faculty of Natural and Applied Sciences, Marian University College, Bagamoyo - Tanzania. His areas of interest are commutative algebra and algebraic geometry.