{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:65YDSJOSUXTS52KDIYPF33PSLV","short_pith_number":"pith:65YDSJOS","schema_version":"1.0","canonical_sha256":"f7703925d2a5e72ee943461e5dedf25d71b7c23cf43f6c38e3f000895268864c","source":{"kind":"arxiv","id":"1309.0279","version":1},"attestation_state":"computed","paper":{"title":"On the Classification of Homogeneous Hypersurfaces in Complex Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexander Isaev","submitted_at":"2013-09-02T00:54:39Z","abstract_excerpt":"We discuss 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 $n=3,7$. We show 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 $n=3,7$. We show 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