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$ N_6$ property for third Veronese embeddings

Author: Thanh Vu
Journal: Proc. Amer. Math. Soc. 143 (2015), 1897-1907
MSC (2010): Primary 13D02, 14M12, 05E10
Published electronically: December 8, 2014
MathSciNet review: 3314100
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Abstract: 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 $ N_6$. This settles the Ottaviani-Paoletti conjecture for third Veronese embeddings. This result is optimal since $ \nu _3({\mathbb{P}}^n)$ does not satisfy the property $ N_7$ for $ n\ge 2$ as shown by Ottaviani-Paoletti.

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Additional Information

Thanh Vu
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720
Address at time of publication: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588

Keywords: Syzygies, Veronese varieties, matching complexes.
Received by editor(s): March 21, 2013
Received by editor(s) in revised form: October 9, 2013
Published electronically: December 8, 2014
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society

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