What happens to a population when its grows larger than its carrying capacity?

basically the size of a population can only grow to equal the amount of resources the environment can provide (carrying capacity). So if there arent many resources in an area and too large of a population, then there will be starvation and fight for resources. But if there is an overabundance of resources and the carrying capacity is very high, then the population will grow till it falls under its own weight. It's the cirlce of life.