Computations in Algebraic Geometry (Macaulay2) by David Eisenbud
Computations in Algebraic Geometry (Macaulay2) - Table of Contents
PART I: INTRODUCING MACAULAY2
1. Ideals, Varieties and Macaulay2
2. Projective Geometry and Homological Algebra
3. Data Types, Functions, and Programming
4. Teaching the Geometry of Schemes
PART II: MATHEMATICAL COMPUTATIONS
5. Monomial Ideals
6. From Enumerative Geometry to Solving Systems of Polynomial Equations
7. Resolutions and Cohomology over Complete Intersections
8. Algorithms for the Toric Hilbert Scheme
9. Sheaf Algorithms Using the Exterior Algebra
10. Needles in a Haystack: Special Varieties via Small Fields
11. D-modules and Cohomology of Varieties
What You Will Learn in Computations in Algebraic Geometry (Macaulay2)
"Computations in Algebraic Geometry (Macaulay2)" by David Eisenbud, Daniel R. Grayson, Michael E. Stillman, and Bernd Sturmfels, is a practical and concept-driven book that connects modern "algebraic geometry" with real computation. Rather than treating geometry as purely theoretical, the book shows how abstract ideas can be explored and tested using "Macaulay2", a powerful computer algebra system designed for research in geometry and commutative algebra.
The book brings together contributions from leading mathematicians and introduces core topics such as "ideals", varieties, resolutions, and cohomology through hands-on computation. Early chapters help readers learn the Macaulay2 language and data structures, while later sections apply these tools to deeper geometric problems. This balance allows readers to move naturally from theory to experimentation, making complex constructions more accessible and concrete.
Aimed at advanced students and researchers, the book is especially valuable for those working at the intersection of "computation" and pure mathematics. It emphasizes algorithms, examples, and executable ideas rather than formal proofs alone. Overall, it serves as both a learning guide and a long-term reference, showing how computational tools can deepen understanding and open new directions in "geometry" and algebraic research.
Book Details & Specifications
Title:
Computations in Algebraic Geometry (Macaulay2) by David Eisenbud
Publisher:
Cambridge University Press
Year:
2001
Pages:
334
Type:
PDF
Language:
English
ISBN-10 #:
B0CWDRVR62
ISBN-13 #:
978-3662048511
License:
External Educational Resource
Amazon:
Amazon
About the Author: David Eisenbud, Daniel R. Grayson, Michael E. Stillman, and Bernd Sturmfels
The author
David Eisenbud, Daniel R. Grayson, Michael E. Stillman, and Bernd Sturmfels
are leading mathematicians known for shaping modern "algebraic geometry" and computational methods. Eisenbud is widely respected for his foundational work in "commutative algebra" and influential mathematical texts. Grayson and Stillman are the creators of "Macaulay2", a major software system for algebraic research, while Sturmfels is known for his work in "computational geometry" and combinatorics. Together, they combine deep theory with "computation", creating a bridge between abstract mathematics and practical experimentation.
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