This is a copy of the arming sword of Henry V (it is very pretty)
An arming sword was a typical one handed sword from the 11th to 16th century. It was light (about 1kg) & quick with a fine point (on this example slightly rounded for safety). People often think that a sword like this would only be good for stabbing but it could just as easily cut and hack with a considerable amount of force.
Arming sword were often worn as a backup weapon, to the lance, mace, warhammer or poleaxe, all of which were more use against armoured knights than a sword.
I occasionally hear people call the groove in the sword a "blood channel" to bleed a victim quicker. No, this is awful Victorian nonsense, the fuller, as it is called, reduces the blades weight while enhancing its structural strength. To see how effective this concave shape is take a flat piece of paper & push it edgeways straight against a wall, now try curving is slightly & try it again. That is what the fuller does.