Curdling is a process by which milk proteins solidify and separate from the whey. Curdling is usually caused by acids, tannins, salt, and heat. The mild acids in many vegetables and the tannins in potatoes are often enough to curdle milk.
Starches partially stabilize milk and cream. This is why it is possible to make soups and sauces with both milk or cream and acid ingredients. Avoid combining milk or cream with strong acids unless a starch is present.
Reducing temperatures and cooking times also helps. Curdling is more likely at high heat or with prolonged cooking.