October 24, 2024
3:30 p.m. CEST
Seminar room - 3rd floor
Abstract Linkage has been used for over a century to study and classify curves in projective three-space and, more generally, varieties in projective space or homogeneous ideals in polynomial rings. Of particular importance have been licci ideals, ideals that can be linked to complete intersection in a finite number of steps. It is known that the Castelnuovo-Mumford regularity of a licci ideal forces a very strict upper bound for the initial degree of the ideal. Now, in joint work with Craig Huneke and Bernd Ulrich, we conjecture that it also bounds the number of generators of the ideal, and we prove this conjecture in many cases. In addition, we provide new sufficient conditions for an ideal to be licci, for classes of ideals of height three and for ideals containing a maximal regular sequence of quadrics. The talk will also explain connections with recent work by Guerrieri, Ni, Weyman and by Jelisiejew, Ramkumar, Sammartano.