Commutative Algebra and Noncommutative Algebraic Geometry: Volume 2, Research Articles

This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 2 focuses on the most recent research.

David Eisenbud (Edited by), Srikanth B. Iyengar (Edited by), Anurag K. Singh (Edited by), J. Toby Stafford (Edited by), Michel Van den Bergh (Edited by)

9781107149724, Cambridge University Press

Hardback, published 19 November 2015

302 pages, 10 b/w illus.
23.4 x 15.6 x 1.8 cm, 0.6 kg

In the 2012–13 academic year, the Mathematical Sciences Research Institute, Berkeley, hosted programs in Commutative Algebra (Fall 2012 and Spring 2013) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013). There have been many significant developments in these fields in recent years; what is more, the boundary between them has become increasingly blurred. This was apparent during the MSRI program, where there were a number of joint seminars on subjects of common interest: birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, and tilting theory, to name a few. These volumes reflect the lively interaction between the subjects witnessed at MSRI. The Introductory Workshops and Connections for Women Workshops for the two programs included lecture series by experts in the field. The volumes include a number of survey articles based on these lectures, along with expository articles and research papers by participants of the programs. Volume 2 focuses on the most recent research.

Preface David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford and Michel Van den Bergh
1. When is a squarefree monomial ideal of linear type? Ali Alilooee and Sara Faridi
2. Modules for elementary abelian groups and hypersurface singularities David J. Benson
3. Ideals generated by superstandard tableaux Andrew Berget, Winfried Bruns and Aldo Conca
4. Zariski topologies on stratified spectra of quantum algebras Kenneth A. Brown and Kenneth R. Goodearl
5. The derived category of a graded Gorenstein ring Jesse Burke and Greg Stevenson
6. Singularities with respect to Mather–Jacobian discrepancies Lawrence Ein and Shihoko Ishii
7. Reduction numbers and balanced ideals Louiza Fouli
8. Unipotent and Nakayama automorphisms of quantum nilpotent algebras Kenneth R. Goodearl and Milen T. Yakilmov
9. Formal fibers of prime ideals in polynomial rings William Heinzer, Christel Rotthaus and Sylvia Wiegand
10. Bounding the socles of powers of squarefree monomial ideals Jürgen Herzog and Takayuki Hibi
11. An intriguing ring structure on the set of d-forms Jürgen Herzog, Leila Sharifan and Matteo Varbaro
12. On the subadditivity problem for maximal shifts in free resolutions Jürgen Herzog and Hema Srinivasan
13. The cone of Betti tables over a rational normal curve Manoj Kummini and Steven V. Sam
14. Adjoint associativity - an invitation to algebra in ?-categories Joseph Lipman.

Subject Areas: Algebraic geometry [PBMW], Algebra [PBF], Mathematics [PB]