Matsusaka's big theorem explained

In algebraic geometry, given an ample line bundle L on a compact complex manifold X, Matsusaka's big theorem gives an integer m, depending only on the Hilbert polynomial of L, such that the tensor power Lⁿ is very ample for n ≥ m.

The theorem was proved by Teruhisa Matsusaka in 1972 and named by Lieberman and Mumford in 1975.^{[1] [2] [3]}

The theorem has an application to the theory of Hilbert schemes.

Notes and References

1. Matsusaka. T.. 1972. Polarized Varieties with a Given Hilbert Polynomial. 2373563. American Journal of Mathematics. 94. 4. 1027–1077. 10.2307/2373563.
2. Book: Lieberman, D.. Algebraic Geometry. Mumford. D.. American Mathematical Society. 1975. Providence, RI. 513 - 530. Matsusaka's big theorem.
3. Kollár, János. János Kollár. Teruhisa Matsusaka (1926–2006). Notices of the American Mathematical Society. August 2006. 53. 7. 766–768.