Six Lectures on Commutative Algebra Book

	Preface
	Infinite Free Resolutions
1	Complexes	4
2	Multiplicative Structures on Resolutions	14
3	Change of Rings	24
4	Growth of Resolutions	34
5	Modules over Golod Rings	44
6	Tate Resolutions	53
7	Deviations of a Local Ring	64
8	Test Modules	75
9	Modules over Complete Intersections	87
10	Homotopy Lie Algebra of a Local Ring	99
	Generic Initial Ideals
1	The Initial Ideal	120
2	Regularity and Saturation	137
3	The Macaulay-Gotzmann Estimates on the Growth of Ideals	147
4	Points in P[superscript 2] and Curves in P[superscript 3]	157
5	Gins in the Exterior Algebra	172
6	Lexicographic Gins and Partial Elimination Ideals	177
	Tight Closure, Parameter Ideals, and Geometry
1	An Introduction to Tight Closure	187
2	How Does Tight Closure Arise?	193
3	The Test Ideal I	200
4	The Test Ideal II: the Gorenstein Case	205
5	The Tight Closure of Parameter Ideals	210
6	The Strong Vanishing Theorem	215
7	Plus Closure	219
8	F-Rational Rings	222
9	Rational Singularities	225
10	The Kodaira Vanishing Theorem	228
	On the Use of Local Cohomology in Algebra and Geometry
1	A Guide to Duality	243
2	A Few Applications of Local Cohomology	259
3	Local Cohomology and Syzygies	276
	Problems and Results on Hilbert Functions of Graded Algebras
1	Macaulay's Theorem	296
2	The Perfect Codimension Two and Gorenstein Codimension Three Case	301
3	The EGH Conjecture	311
4	Hilbert Function of Generic Algebras	317
5	Fat Points: Waring's Problem and Symplectic Packing	319
6	The HF of a CM Local Ring	329
	Cohomological Degrees of Graded Modules
1	Arithmetic Degree of a Module	349
2	Reduction Number of an Algebra	357
3	Cohomological Degree of a Module	364
4	Regularity versus Cohomological Degrees	377
5	Cohomological Degrees and Numbers of Generators	380
6	Hilbert Functions of Local Rings	381
7	Open Questions	389
	Index	393