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On Surfaces Whose Canonical System is Hyperelliptic

  • Patrick Du Val

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On a surface F of genus p g = p a = p and linear genus p (1) = n + 1 whose canonical system is irreducible, and which we shall ordinarily think of as simple and free from exceptional curves, the characteristic series of the canonical system is a semicanonical since the adjoint system of the canonical system is its double, so that the canonical series on a curve of the canonical system is its characteristic series doubled.

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References

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1. Castelnuovo, G., Sidle superficie algebriche le cui sezioni plane sono curve iperellittiche, Rendiconti Circ. Mat. Palermo, vol. 4 (1890), 7388.
2. Castelnuovo, G., Sulle superficie algebriche le cui sezioni sono curve di genere 3, Atti Accad. Torino, vol. 25 (1890), 465484.
3. Conforto, F., Le superficie razionali (Bologna, 1939).
4. Du Val, P., On regular surfaces in space of three dimensions whose plane sections are of genus 4, J. London Math. Soc, vol. 9 (1933), 1118.
5. Du Val, P., On the discovery of linear systems of plane curves of given genus, J. London Math. Soc, vol. 10 (1934), 711.
6. Du Val, P., On isolated singularities of algebraic surfaces which do not affect the conditions of adjunction (III), Proc. Cambridge Phil. Soc, vol. 30 (1934), 483491.
7. Du Val, P., On the Kantor group of a set of points in a plane, Proc. London Math. Soc (2), vol. 32 (1936), 1851.
8. Du Val, P., On absolute and non-absolute singularities of algebraic surfaces, Rev. Fac Sci. Istanbul (A), vol. 9 (1944), 159215.
9. Enriques, F., Le superficie algebriche (Bologna, 1949).
10. Jongmans, F., Mémoire sur les surfaces et les variétés algébriques à courbes sections de genre quatre,Mém. Acad. R. Belg. (cl. sci.) (2), vol. 23, no. 4 (1949).
11. Jongmans, F. and Nollet, L., Classification des systémes linéaires de courbes algébriques planes de genre trois, Mém. Acad. R. Belg. (cl. sci.) (2), vol. 24, no. 6 (1949).
12. Minkowski, H., Raum und Zeit, Jber. dtsch. MatVer., vol. 18 (1909), 7588.
13: Roth, L., On surfaces of sectional genus four, Proc. Cambridge Phil. Soc, vol. 29 (1933), 184194.
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