Cones of divisors on $\mathbb{P}^3$ blown up at eight very general points

Isabel Stenger; Zhixin Xie

Cones of divisors on $\mathbb{P}^3$ blown up at eight very general points

Algebraic Geometry 2023-05-18 v2

Authors: Isabel Stenger , Zhixin Xie

Abstract

Let $X$ be the blowup of $\mathbb{P}^3$ at eight very general points. We give a complete description of its nef and effective cones. Moreover, we show that there exists a rational polyhedral fundamental domain for the action of a certain Weyl group on the effective movable cone of $X$ .

Keywords

blowup divisor cones nef cone effective cone weyl group movable cone

Cite

@article{arxiv.2303.12005,
  title  = {Cones of divisors on $\mathbb{P}^3$ blown up at eight very general points},
  author = {Isabel Stenger and Zhixin Xie},
  journal= {arXiv preprint arXiv:2303.12005},
  year   = {2023}
}

Comments

36 pages. We added Theorem 3.5 and extended Theorem 1.4 by showing that the effective cone is closed

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