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This article is motivated by the authors’ interest in the geometry of the Mori dream space P^4 blown up in 8 general points. In this article, we develop the necessary technique for determining Weyl orbits of linear cycles for the four-dimensional case, by explicit computations in the Chow ring of the resolution of the standard Cremona transformation. In particular, we close this paper with applications to the question of the dimension of the space of global sections of effective divisors having at most 8 points.
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Weyl cycles on the blow up of P^4 at eight points
We define the Weyl cycles on X_n^ s , the blown-up projective space P^n in s points in general position. In particular, we focus on the Mori Dream spaces X3 7 and X4 8, where we classify all the Weyl cycles of codimension two. We further introduce the Weyl expected dimension for the space of global sections of any effective divisor that generalizes the linear expected dimension of [ 2] and the secant expected dimension of [ 4].
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- Award ID(s):
- 2152130
- PAR ID:
- 10514983
- Publisher / Repository:
- Birkhauser, Springer
- Date Published:
- Journal Name:
- Trends in mathematics
- ISSN:
- 2297-0215
- ISBN:
- 978-3-031-11938-5
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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