Right! Kysa, you can check out the Blade Geometry FAQ to find out more.
The hollow grinds that flare out thick at the bottom -- like on a typical Buck -- I don't find particularly excel at anything. They have the non-linear expansion of a hollow-ground knife that disrupts deep cutting, but they lose the edge-thinness advantage of the type of hollow grind I'll describe below.
If you don't flare the ends out, you get a hollow grind like the Sebenza. Here the edge ends up very thin, and we should all know by now thin edges cut VERY well. This gives a performance advantage for shallow cutting. Of course, this type of thin edge will also be more susceptible to rolling or chipping. As Cliff pointed out, the hollow grind doesn't do well for deep cutting. The non-linear expansion of the grind as you get nearer the spine tends to wedge and cut inefficiently. So this type of hollow grind is good for optimum shallow cutting performance where edge strength is not the top concern.
The full flat grind (from spine to edge) also has a thin edge, but not quite as thin as the hollow grind. For shallow cuts, it will not cut quite as well, but will be stronger. For deeper cuts, the flat grind really excels. There's a reason why kitchen knives are usually a full flat grind -- this grind really works for deep cuts of all kinds. So the flat grind loses a little shallow-cutting performance, but gains strength and deep-cutting performance.
A sabre grind, which is a flat grind that starts from the middle of the blade instead of the spine, gains even more in strength, but suffers in cutting performance for both deep and shallow cuts.
I've completely ignored niche jobs like splitting, where you want a rapid increase in width to split (say) kindling.
Joe
jat@cup.hp.com