Abstract: The rational homology groups of the matching complexes are closely related to the syzygies of the Veronese embeddings. In this talk, I will give a proof of the shellability of certain skeleta of matching complexes, thus proving that the coordinate rings of the Veronese varieties satisfy property $N_{2d-2}$. Using duality and explicit computation of homology groups of matching complexes, we will deduce the Ottaviani-Paoletti conjecture for fourth Veronese embeddings.
Seminar
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