Titlebook: Computations in Algebraic Geometry with Macaulay 2; David Eisenbud,Michael Stillman,Bernd Sturmfels Textbook 2002 Springer-Verlag Berlin H

Chagrin

Robert S. Sheldon,Satish R. RajIn this chapter we explain constructive methods for computing the cohomology of a sheaf on a projective variety. We also give a construction for the Beilinson monad, a tool for studying the sheaf from partial knowledge of its cohomology. Finally, we give some examples illustrating the use of the Beilinson monad.

Constant

emulsify

慢慢啃

integral

Data Types, Functions, and ProgrammingIn this chapter we present an introduction to the structure of . commands and the writing of functions in the . language. For further details see the . manual distributed with the program [1].

Omnipotent

Teaching the Geometry of SchemesThis chapter presents a collection of graduate level problems in algebraic geometry illustrating the power of . as an educational tool.

Accolade

Monomial IdealsMonomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in . for studying and using monomial ideals. We illustrate these methods with examples from combinatorics, integer programming, and algebraic geometry.

GIST

節(jié)省

-modules and Cohomology of VarietiesIn this chapter we introduce the reader to some ideas from the world of differential operators. We show how to use these concepts in conjunction with . to obtain new information about polynomials and their algebraic varieties.

arboretum

Computations in Algebraic Geometry with Macaulay 2978-3-662-04851-1Series ISSN 1431-1550