General quadratic optimization problems with linear constraints and additional indicator constraints on the variables are studied. Based on the well-known perspective reformulation for mixed-integer quadratic optimization problems, projective cuts are introduced as new valid inequalities for the general problem. The key idea behind the theory of these cutting planes is the projection of the continuous variables onto the space of optimal solutions dependent on the choice of indicator variables. The advantages of projective cutting planes for practical computations are illustrated with a numerical study of uncapacitated facility location problems.