arXiv Open Access 2017

Mapping properties of the Hilbert and Fubini--Study maps in Kähler geometry

Yoshinori Hashimoto
Lihat Sumber

Abstrak

Suppose that we have a compact Kähler manifold $X$ with a very ample line bundle $\mathcal{L}$. We prove that any positive definite hermitian form on the space $H^0 (X,\mathcal{L})$ of holomorphic sections can be written as an $L^2$-inner product with respect to an appropriate hermitian metric on $\mathcal{L}$. We apply this result to show that the Fubini--Study map, which associates a hermitian metric on $\mathcal{L}$ to a hermitian form on $H^0 (X,\mathcal{L})$, is injective.

Topik & Kata Kunci

Penulis (1)

Y

Yoshinori Hashimoto

Format Sitasi

Hashimoto, Y. (2017). Mapping properties of the Hilbert and Fubini--Study maps in Kähler geometry. https://arxiv.org/abs/1705.11025

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2017
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓