{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HYORDIFNRXBGUJAX46KPF4QCAY","short_pith_number":"pith:HYORDIFN","schema_version":"1.0","canonical_sha256":"3e1d11a0ad8dc26a2417e794f2f20206058d3e0fdb41e6bf23290de00930d908","source":{"kind":"arxiv","id":"1610.07270","version":2},"attestation_state":"computed","paper":{"title":"On homogeneous hypersurfaces in ${\\mathbb C}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexander Isaev","submitted_at":"2016-10-24T03:06:19Z","abstract_excerpt":"We consider a family $M_t^n$, with $n\\ge 2$, $t>1$, of real hypersurfaces in a complex affine $n$-dimensional quadric arising in connection with the classification of homogeneous compact simply-connected real-analytic hypersurfaces in ${\\mathbb C}^n$ due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the embeddability of $M_t^n$ in ${\\mathbb C}^n$ for $n=3,7$. In our earlier article we showed that $M_t^7$ is not embeddable in ${\\mathbb C}^7$ for every $t$ and that $M_t^3$ is embeddable in ${\\mathbb C}^3$ for all $11$, of real hypersurfaces in a complex affine $n$-dimensional quadric arising in connection with the classification of homogeneous compact simply-connected real-analytic hypersurfaces in ${\\mathbb C}^n$ due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the embeddability of $M_t^n$ in ${\\mathbb C}^n$ for $n=3,7$. In our earlier article we showed that $M_t^7$ is not embeddable in ${\\mathbb C}^7$ for every $t$ and that $M_t^3$ is embeddable in ${\\mathbb C}^3$ for all $1