Non-quasi-projective moduli spaces


We show that every smooth toric variety (and many other algebraic spaces as well) can be realized as a moduli space for smooth, projective, polarized varieties. Some of these are not quasi-projective. This contradicts a recent paper (Quasi-projectivity of moduli spaces of polarized varieties, Ann. of Math.159 (2004) 597–639.).


János Kollár

Department of Mathematics, Princeton University, Princeton, NJ 08544, United States