why do desert and arctic tundra support smaller biomass of animals than tropical forest?

Answer 1

A physics answer is that there is more energy supplied to a tropical forest (in the form of more sunlight, and higher overall temperature). More sunlight energy means more plant growth, and so on, down the food chain.

Answer 2

Differences in primary productivity. Larger numbers of primary producers (e.g., plants) the more biomass of herbivores it can support.