We prove bounds on the saturation degrees of homogeneous ideals (and their powers) defining smooth complex projective varieties. For example, we show that a classical statement due to Macaulay for zero-dimensional complete intersection ideals holds for any smooth variety. For curves, we bound the saturation degree of powers in terms of the regularity.
"Saturation bounds for smooth varieties." Algebra Number Theory 16 (6) 1531 - 1546, 2022. https://doi.org/10.2140/ant.2022.16.1531