Constructing distinct curves with isomorphic Jacobians in characteristic zero

International Mathematics Research Notices

Volumn 1995, Issue 4, 1995, Pages 173-180

  Howe, Everett W ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039827971     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/S1073792895000134     Document Type: Article

References (10)

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2. C. Ciliberto and G. van der Geer, –Non-isomorphic curves of genus four with isomorphic (nonpolarized) Jacobians— in Classification of Algebraic Varieties, ed. by C. Ciliberto, E. L. Livorni, and A. J. Sommese, Contemp. Math. 162, Amer. Math. Soc., Providence, 1994, 129-133.
3. T. Hayashida, A class number associated to the product of an elliptic curve with itself, J. Math. Soc. Japan 20 (1968), 26-43.
4. T. Hayashida and M. Nishi, Existence of curves of genus 2 on a product of elliptic curves, J. Math. Soc. Japan 17 (1965), 1-16.
5. E. W. Howe, Constructing distinct curves with isomorphic Jacobians, to appear in J. Number Theory.
6. G. Humbert, Sur les fonctiones abeliennes singulières (deuxième memoire), J. Math. Pures Appl. (5) 6 (1900), 279-386.
7. H. Lange, Abelian varieties with several principal polarizations, Duke Math. J. 55 (1987), 617-628.
8. H. Lange and Ch. Birkenhake, Complex Abelian Varieties, Grundlehren Math. Wiss. 302, Springer-Verlag, New York, 1992.
9. H. W. Lenstra, Jr., Complex multiplication structure ofelliptic curves, to appear in J. Number Theory.
10. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten, Tokyo, 1971.