$N_6$ property for third Veronese embeddings
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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.References
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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
- Email: vqthanh@math.berkeley.edu
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 1897-1907
- MSC (2010): Primary 13D02, 14M12, 05E10
- DOI: https://doi.org/10.1090/S0002-9939-2014-12396-3
- MathSciNet review: 3314100