2021/04/29 by Lorenzo Barban, Barban, Lorenzo, Eleonora A. Romano +1
Mathematics · #14L30 #14M25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Primary 14E05 #Secondary 14M17
paper · pdf · doi:10.48550/arxiv.2104.14442
openalex publication_date 2021/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from ℂ^*-actions on complex projective varieties, we construct and investigate birational maps among the corresponding extremal fixed point components. We study the case in which such birational maps are locally described by toric flips, either of Atiyah type or so called non-equalized. We relate this notion of toric flip with the property of the action being non-equalized. Moreover, we find explicit examples of rational homogeneous varieties admitting a ℂ^*-action whose weighted blow-up at the extremal fixed point components gives a birational map among two projective varieties that is locally a toric non-equalized flip.