Liaison Theory and Related Problems in Commutative Algebra

Liaison (or linkage) theory is an improtant area in the overlap between algebraic geometry and commutative algebra, and is listed in both subjects in the 2010 MSC (12C40 and 14M06). This proposal involves both faces of liaison theory: the theory and applications to other problems in commutative algevra. We propose a new direction on the theoretical side that we expect will generate contributions by many researchers, and we propose a number of problems that although they may involve liaison to different extents, still will be approached from the perspective, and with the tools, that we have developed over the years in studying liaison.