Intersection of two quadrics with no common hyperplane in P n (Fq)
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چکیده
Let Q1 and Q2 be two arbitrary quadrics with no common hyperplane in P n(Fq). We give the best upper bound for the number of points in the intersection of these two quadrics. Our result states that |Q1 ∩ Q2| ≤ 4q n−2 + πn−3. This result inspires us to establish the conjecture on the number of points of an algebraic set X ⊂ Pn(Fq) of dimension s and degree d: |X(Fq)| ≤ dq s + πs−1.
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تاریخ انتشار 2009