The Geometry of Syzygies Page 1 The Geometry of Syzygies A second course in Commutative
Algebra and Algebraic Geometry David Eisenbud University of California, Berkeley with the …

Determinantal rings and varieties have been a central topic of commutative algebra and
algebraic geometry for several decades. Numerous researchers have contributed to the …

Let S= k [x,,..., x,] be a polynomial ring over a field and let A4=@,*-a, M, be a finitely
generated graded module; in the most interesting case A4 is an ideal of S. For a given …

Modern developments in representation theory rely heavily on homological methods. This
book for advanced graduate students and researchers introduces these methods from their …

Let $ Q $ be a quiver without oriented cycles. For a dimension vector $\beta $ let
$\operatorname {Rep}(Q,\beta) $ be the set of representations of $ Q $ with dimension …

We derive an explicit version of the Bernstein-Gel'fand-Gel'fand (BGG) correspondence
between bounded complexes of coherent sheaves on projective space and minimal doubly …

J. Emsalem and the author showed in [18] that a general polynomial $ f $ of degree $ j $ in
the ring $\mathcal {R}= k [{{y_1},\ldots,{y_r}}] $ has $\left ({\begin {array}{*{20}{c}}{j+ r-1}\\{r …

Green gives an extensive account of the representation theory of Schur algebras in his
recent monograph [171. These algebras provide a convenient framework for discussing the …

Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and
problems. This side of the subject can be approached through the equations of a variety …

We construct virtual fundamental classes for dg–manifolds whose tangent sheaves have
cohomology only in degrees 0 and 1. This condition is analogous to the existence of a …