Seshadri Constant

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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*<sup>*k*</sup>. 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**.

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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

- Robert Lazarsfeld,
*Positivity in Algebraic Geometry I: Classical Setting*(2004), pp. 269–70

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