Cones of Cycles on blowups of $({\mathbb P}^1)^n$

Gilberto Bini; Luca Ugaglia

Cones of Cycles on blowups of $({\mathbb P}^1)^n$

Algebraic Geometry 2025-03-04 v2

Authors: Gilberto Bini , Luca Ugaglia

Abstract

We study cones of pseudoeffective cycles on the blow up of $({\mathbb P}^1)^n$ at points in very general position, proving some results concerning their structure. In particular we show that in some cases they turn out to be generated by exceptional classes and fiber classes relatively to the projections onto a smaller number of copies of projective lines.

Keywords

algebraic geometry cone of cycles blowup projective space exceptional divisor

Cite

@article{arxiv.2405.11638,
  title  = {Cones of Cycles on blowups of $({\mathbb P}^1)^n$},
  author = {Gilberto Bini and Luca Ugaglia},
  journal= {arXiv preprint arXiv:2405.11638},
  year   = {2025}
}

Comments

14 pages. Final version to appear in Collectanea Mathematica

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