The approach of Stöhr-Voloch to the Hasse-Weil bound with applications to optimal curves and plane arcs
نویسندگان
چکیده
1. Linear series on curves 1.1. Terminology and notation 1.2. Morphisms from linear series; Castelnuovo’s genus bound 1.3. Linear series from morphisms 1.4. Relation between linear series and morphisms 1.5. Hermitian invariants; Weierstrass semigroups I 2. Weierstrass point theory 2.1. Hasse derivatives 2.2. Order sequence; Ramification divisor 2.3. D-Weierstrass points 2.4. D-osculating spaces 2.5. Weierstrass points; Weierstrass semigroups II 3. Frobenius orders 4. Optimal curves 4.1. A Fq-divisor from the Zeta Function 4.2. The Hermitian curve 4.3. The Suzuki curve 5. Plane arcs 5.1. B. Segre’s fundamental theorem: Odd case 5.2. The work of Hirschfeld, Korchmáros and Voloch
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