Projective geometry and homological algebra

@inproceedings{Eisenbud2002ProjectiveGA,
  title={Projective geometry and homological algebra},
  author={David Eisenbud},
  year={2002}
}
We provide an introduction to many of the homological commands in Macaulay 2 (modules, free resolutions, Ext and Tor. ..) by means of examples showing how to use homological tools to study projective varieties. 
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4 Citations

Computing Amoebas
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This work gives explicit characterizations for the amoebas of classes of linear and nonlinear varieties and presents homotopy-based techniques to compute the boundary of two-dimensional amoEBas.
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This expository paper describes the solutions to several enumerative problems involving conies, including Steiner's problem, and uses these problems to introduce and demonstrate several of the key ideas and tools of algebraic geometry.
Some Non-Unimodal Level Algebras
In 2005, building on his own recent work and that of F. Zanello, A. Iarrobino discovered some constructions that, he conjectured, would yield level algebras with non-unimodal Hilbert functions. This…
Some new non-unimodal level algebras

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So far only six families of smooth irregular surfaces are known to exist in P^4 (up to pullbacks by suitable finite covers of P^4). These are the elliptic quintic scrolls, the minimal abelian and…
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Syzygies of canonical curves and special linear series
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On the projective normality of complete linear series on an algebraic curve
Algèbre locale : multiplicités
Non-general Type Surfaces in P4: Some Remarks on Bounds and Constructions
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