### The Manin-Peyre conjectures for an infinite family of projective hypersurfaces in higher dimension.

Heilbronn Number Theory Seminar

8th November 2017, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

For a projective variety containing infinitely many rational points, a natural question is to

count the number of such points of height less than some bound B. The Manin-Peyre

conjectures predict, for Fano varieties, an asymptotic formula for this number as B goes

to infinity in terms of geometric invariants of the variety. We will discuss in this talk the

Manin-Peyre’s conjectures for the family of varieties given by the equation

x1y2y3 · · · yn + x2y1y3 · · · yn + · · · + xny1y2 · · · yn−1 = 0 (for n >= 2).

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