Rajib Sarkar
TIFR, Mumbai
November 25, 2021
Castelnuovo-Mumford Regularity of Quadratic Sequences with applications to Binomial Ideals: 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.
TIFR, Mumbai
November 25, 2021
Castelnuovo-Mumford Regularity of Quadratic Sequences with applications to Binomial Ideals: 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.