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Curves containing all points of a finite projective Galois plane. (English) Zbl 1428.14052
Summary: In the projective plane $$P G(2, q)$$ over a finite field of order $$q$$, a Tallini curve is a plane irreducible (algebraic) curve of (minimum) degree $$q + 2$$ containing all points of $$P G(2, q)$$. Such curves were investigated by G. Tallini [Rend. Mat. Appl., V. Ser. 20, 431–479 (1961; Zbl 0106.35604); Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 30, 706–712 (1961; Zbl 0107.38104)], and by M. Homma and S. J. Kim [Linear Algebra Appl. 438, No. 3, 969–985 (2013; Zbl 1259.14023)]. Our results concern the automorphism groups, the Weierstrass semigroups, the Hasse-Witt invariants, and quotient curves of the Tallini curves.

##### MSC:
 14H50 Plane and space curves 14H25 Arithmetic ground fields for curves 14G15 Finite ground fields in algebraic geometry
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##### References:
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