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

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arxiv 2303.12005 v3 pith:DSUZZJP4 submitted 2023-03-21 math.AG

Isabel Stenger , Zhixin Xie This is my paper · ORCID

classification math.AG

keywords coneseffectiveeightgeneralmathbbpointsveryaction

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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 $X$.

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Blowups, Gale duality, and moduli spaces
math.AG 2026-05 unverdicted novelty 7.0 of 10

The K-negative part of the effective cone of the blowup of P^n at n+4 general points is generated by the Weyl-group orbit of one exceptional divisor, and the movable cone decomposes into Mori chambers.

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