Poncelet's theorem in space

Author:
Emma Previato

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2547-2556

MSC (1991):
Primary 14H40; Secondary 58F07

Published electronically:
May 4, 1999

MathSciNet review:
1662198

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Abstract | References | Similar Articles | Additional Information

Abstract: A plane polygon inscribed in a conic and circumscribed to a conic can be continuously `rotated', as it were. One of the many proofs consists in viewing each side of as translation by a torsion point of an elliptic curve. In the -space version, involving torsion points of hyperelliptic Jacobians, there is a -dimensional family of rotations, where of the hyperelliptic curve; the polygon is now inscribed in one and circumscribed to quadrics.

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Additional Information

**Emma Previato**

Affiliation:
Department of Mathematics, Boston University, Boston, Massachusetts 02215

Email:
ep@math.bu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05307-1

Received by editor(s):
May 20, 1997

Received by editor(s) in revised form:
September 28, 1997

Published electronically:
May 4, 1999

Additional Notes:
The author’s research was partly supported by NSA grant MDA904-95-H-1031

Communicated by:
Ron Donagi

Article copyright:
© Copyright 1999
American Mathematical Society