N6 PROPERTY 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 settles the Ottaviani-Paoletti conjecture for third Veronese embeddings. This result is optimal since V3 (Pn) does not satisfy the property N7 for n > 2 as shown by Ottaviani-Paoletti. [ABSTRACT FROM AUTHOR]