Let X be a smooth projective surface of irregularity 0. The Hilbert scheme X[n] of n points on X parametrizes zero-dimensional subschemes of X of length n. We discuss general methods for studying the cone of ample divisors on X[n]. We then use these techniques to compute the cone of ample divisors on X[n] for several surfaces where the cone was previously unknown. Our examples include families of surfaces of general type and del Pezzo surfaces of degree 1. The methods rely on Bridgeland stability and the positivity lemma of Bayer and Macrì.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory