A compactification of a family of determinantal Godeaux surfaces. (English) Zbl 0952.14029
Summary: We present a geometric description of the compactification of the family of determinantal Godeaux surfaces, via the study of the bicanonical pencil and using classical Prym theory. In particular, we reduce the problem of compactifying the space of bicanonical pencils of determinantal Godeaux surfaces to the compactification of the family of twisted cubic curves in \(\mathbb{P}^{3}\) with certain given tangent conditions.
MSC:
| 14J29 | Surfaces of general type |
| 32J05 | Compactification of analytic spaces |
| 14J10 | Families, moduli, classification: algebraic theory |
| 14M12 | Determinantal varieties |
Keywords:
compactification of the family of determinantal Godeaux surfaces; bicanonical pencil; Prym theoryReferences:
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