The Genus of Space Curves.
Joe Harris (1980)
Mathematische Annalen
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Joe Harris (1980)
Mathematische Annalen
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Nils Bruin, E. Victor Flynn, Damiano Testa (2014)
Acta Arithmetica
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We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.
L. Chiantini, C. Ciliberto (1995)
Manuscripta mathematica
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Edoardo Ballico, N. Chiarli, S. Greco (2004)
Collectanea Mathematica
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We find some ranges for the 4-tuples of integers (d,g,n,r) for which there is a smooth connected non-degenerate curve of degree d and genus g, which is k-normal for every k ≤ r.
Kenji Ueno, Y. Namikawa (1973)
Manuscripta mathematica
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Yukihiro Uchida (2011)
Acta Arithmetica
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Arnaldo Garcia (1986)
Manuscripta mathematica
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Shigeaki Tsuyumine (1991)
Mathematische Zeitschrift
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Angelo Felice Lopez, Gian P. Pirola (1995)
Mathematische Zeitschrift
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Lomont, Chris (2002)
Experimental Mathematics
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Gerhard Rosenberger, Norman Purzitsky (1972)
Mathematische Zeitschrift
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Luis Giraldo, Ignacio Sols (1998)
Collectanea Mathematica
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Let S be a ruled surface in P3 with no multiple generators. Let d and q be nonnegative integers. In this paper we determine which pairs (d,q) correspond to the degree and irregularity of a ruled surface, by considering these surfaces as curves in a smooth quadric hypersurface in P5.
Fernando Cukierman, Douglas Ulmer (1993)
Compositio Mathematica
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