English

The geometry of Hilbert schemes of two points on projective space

Algebraic Geometry 2021-03-24 v1

Abstract

In this paper, we give three bases for the cohomology groups of the Hilbert scheme of two points on projective space. Then, we use these bases to compute all effective and nef cones of higher codimensional cycles on the Hilbert scheme. Next, we compute the class in one of these bases of the Chern classes of tautological bundles coming from line bundles. Finally, we provide an application of these results to the degrees of secant varieties of complete intersections.

Keywords

Cite

@article{arxiv.2103.12674,
  title  = {The geometry of Hilbert schemes of two points on projective space},
  author = {Tim Ryan},
  journal= {arXiv preprint arXiv:2103.12674},
  year   = {2021}
}

Comments

16 pages, 3 tables, comments welcome!