Rolling Factors Deformations and Extensions of Canonical Curves

A tetragonal canonical curve is the complete intersection of two divisors on a scroll. The equations can be written in `rolling factors' format. For such homogeneous ideals we give methods to compute infinitesimal deformations. Deformations can be obstructed. For the case of quadratic equations on the scroll we derive explicit base equations. They are used to study extensions of tetragonal curves.

2000 Mathematics Subject Classification: 14B07 14H51 14J28 32S30

Keywords and Phrases: Tetragonal curves, rolling factors, K3 surfaces

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