Seshadri constant

In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle "L" at a point "P" on an algebraic variety. It was introduced by Demailly to measure a certain "rate of growth", of the tensor powers of "L", in terms of the jets of the sections of the "L""k". The object was the study of the Fujita conjecture.
The name is in honour of the Indian mathematician C. S. Seshadri.
It is known that Nagata's conjecture on algebraic curves is equivalent to the assertion that for more than nine general points, the Seshadri constants of the projective plane are maximal. There is a general conjecture for algebraic surfaces, the Nagata–Biran conjecture.
Definition.
Let formula_1 be a smooth projective variety, formula_2 an ample line bundle on it, formula_3 a point of formula_1, formula_5 = { all irreducible curves passing through formula_3 }.
formula_7.
Here, formula_8 denotes the intersection number of formula_2 and formula_10, formula_11 measures how many times formula_10 passing through formula_3.
Definition: One says that formula_14 is the Seshadri constant of formula_2 at the point formula_3, a real number. When formula_1 is an abelian variety, it can be shown that formula_14 is independent of the point chosen, and it is written simply formula_19.