Birational Transformations on Irreducible Compact Hermitian Symmetric Spaces

We construct a sequence of explicit blow-ups and blow-downs on an 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. The result was known in the special case where X is of rank 2 and could be found in Zak’s monograph “Tangents and secants of algebraic varieties.”