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The surfaces whose prime-sections contain a
| Content Provider | Scilit |
|---|---|
| Author | Bronowski, J. |
| Copyright Year | 1934 |
| Description | The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order $4_{p}$ + 4 and lie in space $[3_{p}$ + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7C55E6CC9C0B2BE31A4989E38229E0D4/S0305004100016583a.pdf/div-class-title-the-surfaces-whose-prime-sections-contain-a-img-mimesubtype-gif-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20151103033210884-0873-s0305004100016583inline1-gif-pub-status-live-img-div.pdf |
| Ending Page | 177 |
| Page Count | 8 |
| Starting Page | 170 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100016583 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 2 |
| Volume Number | 30 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1934-04-30 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Surfaces Whose Prime Sections |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
