COMMUTATIVE ALGEBRA AND NONCOMMUTATIVE ALGEBRAIC GEOMETRY VOL 2

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.

• High-quality articles survey the current state of knowledge in this extremely active field.
• Focuses on areas of common interest which emphasise the lively interaction between commutative algebra and noncommutative algebraic geometry.
• Valuable to researchers and graduate students studying algebra and algebraic geometry.

Authors
• David Eisenbud, University of California, Berkeley. Professor in the Department of Mathematics at the University of California, Berkeley.
• Srikanth B. Iyengar, University of Utah. Professor in the Department of Mathematics at the University of Utah.
• Anurag K. Singh, University of Utah. Professor in the Department of Mathematics at the University of Utah.
• J. Toby Stafford, University of Manchester. Professor in the Department of Mathematics at the University of Manchester.
• Michel Van den Bergh, Fonds Wetenschappelijk Onderzoek (FWO), Belgium. Director of Research at the Research Foundation - Flanders (FWO) in Belgium.

Table of Contents
Preface.
1. When is a squarefree monomial ideal of linear type?.
2. Modules for elementary abelian groups and hypersurface singularities.
3. Ideals generated by superstandard tableaux.
4. Zariski topologies on stratified spectra of quantum algebras.
5. The derived category of a graded Gorenstein ring.
6. Singularities with respect to Mather–Jacobian discrepancies.
7. Reduction numbers and balanced ideals.
8. Unipotent and Nakayama automorphisms of quantum nilpotent algebras.
9. Formal fibers of prime ideals in polynomial rings.
10. Bounding the socles of powers of squarefree monomial ideals.
11. An intriguing ring structure on the set of d-forms.
12. On the subadditivity problem for maximal shifts in free resolutions.
13. The cone of Betti tables over a rational normal curve.
14. Adjoint associativity - an invitation to algebra in.