Weyl cycles on the blow-up of ${\mathbb{P}}^4$ at eight points

Abstract

We define the Weyl cycles on $X_s^n$, the blown up projective space ${\mathbb{P}}^n$ in $s$ points in general position. In particular, we focus on the Mori Dream spaces $X_7^3$ and $X_8^4$, where we classify all the Weyl cycles of codimension two. We further introduce the Weyl expected dimension for the space of the global sections of any effective divisor that generalizes the linear expected dimension and the secant expected dimension.

Final version, published in The Art of Doing Algebraic Geometry. Trends in Mathematics. Birkhauser, Cham (2023)

References in corpus (2)

• Effective cones of cycles on blow-ups of projective space
• On the Fano variety of linear spaces contained in two odd-dimensional quadrics