Syzygies of Quadratic Veronese Embedding

Abstract

In this work we explicitly calculate syzygies of quadratic Veronese embedding $\mathbb{P}(V)\subset \mathbb{P}({\mathrm{Sym}}^{2}V)$ as representations of the group $\mathrm{GL}(V)$. Also resolutions of the sheaves ${\mathcal{O}}_{\mathbb{P}(V)}(i)$ are constructed in the category $D(\mathbb{P}({\mathrm{Sym}}^{2}V))$.

20 pages, 6 figures

References in corpus (1)

• Syzygy algebras for the Segre embeddings