On highly degenerate CR maps of spheres
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913329363025920 |
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| author | della Sala, Giuseppe Lamel, Bernhard Reiter, Michael Son, Duong Ngoc |
| author_facet | della Sala, Giuseppe Lamel, Bernhard Reiter, Michael Son, Duong Ngoc |
| contents | For $N \geq 4$ we classify the $(N-3)$-degenerate smooth CR maps of the three-dimensional unit sphere into the $(2N-1)$-dimensional unit sphere. Each of these maps has image being contained in a five-dimensional complex-linear space and is of degree at most two, or equivalent to one of the four maps into the five-dimensional sphere classified by Faran. As a byproduct of our classification we obtain new examples of rational maps of degree three which are $(N-3)$-degenerate only along a proper real subvariety and are not equivalent to polynomial maps. In particular, by changing the base point, it is possible to construct new families of nondegenerate maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13525 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On highly degenerate CR maps of spheres della Sala, Giuseppe Lamel, Bernhard Reiter, Michael Son, Duong Ngoc Complex Variables 32H02, 32V40 For $N \geq 4$ we classify the $(N-3)$-degenerate smooth CR maps of the three-dimensional unit sphere into the $(2N-1)$-dimensional unit sphere. Each of these maps has image being contained in a five-dimensional complex-linear space and is of degree at most two, or equivalent to one of the four maps into the five-dimensional sphere classified by Faran. As a byproduct of our classification we obtain new examples of rational maps of degree three which are $(N-3)$-degenerate only along a proper real subvariety and are not equivalent to polynomial maps. In particular, by changing the base point, it is possible to construct new families of nondegenerate maps. |
| title | On highly degenerate CR maps of spheres |
| topic | Complex Variables 32H02, 32V40 |
| url | https://arxiv.org/abs/2210.13525 |