N6PROPERTY FOR THIRD VERONESE EMBEDDINGS

N6PROPERTY FOR THIRD VERONESE EMBEDDINGS

The rational homology groups of the matching complexes are closely related to the syzygies of the Veronese embeddings. In this paper we will prove the vanishing of certain rational homology groups of matching complexes, thus proving that the third Veronese embeddings satisfy the property N6. This se...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2015-05, Vol.143 (5), p.1897-1907
1. Verfasser: VU, THANH
Format: Artikel
Sprache:eng
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Zusammenfassung:The rational homology groups of the matching complexes are closely related to the syzygies of the Veronese embeddings. In this paper we will prove the vanishing of certain rational homology groups of matching complexes, thus proving that the third Veronese embeddings satisfy the property N6. This settles the Ottaviani-Paoletti conjecture for third Veronese embeddings. This result is optimal since ν3(ℙn) does not satisfy the property N7 for n ≥ 2 as shown by Ottaviani-Paoletti.
ISSN:0002-9939
1088-6826