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Addendum/Erratum to the paper "Weyl groups and Birational transformations among minimal models"

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arxiv 2401.13431 v1 pith:J2DXZJWT submitted 2023-10-23 math.AG

classification math.AG
keywords groupsweylfanoaddendumassociatingbirationalerratumfolds
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abstract

We present an addendum/erratum to the paper "Weyl Groups and Birational Transformations among Minimal Models" written by the author and published in 1995, adding the analysis of the "88-th" deformation type of a smooth Fano 3-fold with $B_2 = 4$ denoted as $n^o\ 13$, which was missing from the original classification table by Mori-Mukai and added later to the list of smooth Fano 3-folds with $B_2 \geq 2$, while correcting the mistake pointed out by Eric Jovinelly (also noticed earlier by Kento Fujita). We also correct other typos and miscalculations, clarifying some points of ambiguity. The original paper is an attempt to generalize the result of Y. Manin associating some Weyl groups to Del Pezzo surfaces to the one associating certain Weyl groups to Fano 3-folds.

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  1. A rationality criterion for real Fano threefolds

    math.AG 2025-07 conditional novelty 7.0 of 10

    For smooth geometrically rational real Fano threefolds with nonempty real locus, the absence of any deformation-equivalent real form with disconnected real locus forces R-rationality.

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