Castelnuovo-Mumford Regularity of Quadratic Sequences with applications to Binomial Ideals

Abstract: Cutkosky-Herzog-Trung and independently Kodiyalam proved that
the Castelnuovo-Mumford regularity of powers of homogeneous ideals in a
polynomial ring is bounded above by a linear function. Given a homogeneous
ideal, finding this linear function is a very difficult task. In this
talk, we will compute the linear function for the ideals generated by
homogeneous quadratic sequences. For this, we will start with the
definition of d-sequence and its generalization to the quadratic sequence.
We then talk about the regularity upper bound of powers of an ideal
generated by a quadratic sequence in terms of its related ideals and
degrees of generators. We then apply these results to the binomial edge
ideals for several computations.