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On triple Veronese embeddings of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {P}^n$\end{document} in the Grassmannians
Author(s) -
Huh Sukmoon
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810234
Subject(s) - embedding , mathematics , combinatorics , corollary , grassmannian , vector bundle , pure mathematics , computer science , artificial intelligence
We classify all the embeddings of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {P}_n$\end{document} in a Grassmannian Gr (1, N ) such that the composition with the Plücker embedding is given by a linear system of cubics on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {P}_n$\end{document} . As a direct corollary, we prove that every vector bundle giving such an embedding, splits if n ⩾ 3. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim