Time: 9h30 – 11h, Tuesday October 8, 2024

Venue: Vietnam Institute for Advance in Mathematics (VIASM)

Abstract: Recently, Ein-Ha-Lazarsfeld proved that if I is a homogeneous ideal whose zero locus is a non-singular complex projective scheme, then the saturation degree sdeg I^n is bounded above by a linear function of n whose slope is less or equal the maximal generating degree of I. Inspired by the asymptotic behavior of the Castelnuovo-Mumford regularity, we show that for an arbitrary graded ideal I in an arbitrary graded ring, sdeg I^n is either a constant or a linear function for n large enough whose slope is one of the generating degrees of I.