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Linear codes What about other surfaces ?

The main idea is to homogenize the polynomial
h(x, y) = (xq − x)fx + (y q − q)fy .

It seems to be possible to generalize this idea to a family of surfaces,
P2 and P1 × P1 are toric surfaces.

toric surfaces.

Toric surfaces are naturally endowed with a graded coordinate ring of polynomials and
Euler identities, two essential ingredients in this method.
Thank you for your attention !

Jade Nardi

Bound on Fq points on a curve in P1 × P1

Tuesday 13 March

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