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arXiv · 2212.03510

Birational transformations on irreducible compact Hermitian symmetric spaces

Cong Ding
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Abstract

We construct a sequence of explicit blow-ups and blow-downs on irreducible compact Hermitian symmetric spaces $X$ which transforms it into a projective space of the same dimension. Moreover this resolves a birational map given by Landsberg and Manivel. Centers of the blow-ups for $X$ are constructed by loci of chains of minimal rational curves and centers of the blow-ups for the projective space are constructed from the variety of minimal rational tangents of $X$ and its higher secant varieties.

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Cong Ding. 2022-12-07. Birational transformations on irreducible compact Hermitian symmetric spaces. https://doi.org/10.1093/imrn%2Frnae045

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