Abstract
This article is motivated by the authors’ interest in the geometry of the Mori dream space \(\mathbb {P}^4\) 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 base points.
The first author is supported by NSF grant DMS1802082.
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The collaboration was partially supported by NSF grant DMS1802082.
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Dumitrescu, O., Miranda, R. (2023). Cremona Orbits in \(\mathbb {P}^4\) and Applications. In: Dedieu, T., Flamini, F., Fontanari, C., Galati, C., Pardini, R. (eds) The Art of Doing Algebraic Geometry. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-11938-5_7
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