The function of the filament is to hold up the anther.Without the filament,the anther will be inside the flower and the pollens on it cannot have any cross-pollination or any self-pollination.(Can't have any offspring)
The filament raises the anther level to or above the anther so that the pollen can drop into the female organ.
2 reasons:
Pollen grains need to travel by wind. The filament allows exposure to the air current. Thus, it increases the chance of pollination.
Plants always do cross-pollination and should never do self-pollination (genetic diversity) so raising the filament is a physical barrier preventing pollen from getting to the same ovule.
It give support to the anther to raises the of anther
Each stamen has 2 parts the stalk, called the filament and the pollen producing organ called the anther.