Syzygy algebras for the Segre embeddings

Abstract

We describe the syzygy spaces for the Segre embedding $\mathbb{P}(U)\times \mathbb{P}(V)\subset \mathbb{P}(U\otimes V)$ in terms of representations of $\mathrm{GL}(U)\times \mathrm{GL}(V)$ and construct the minimal resolutions of the sheaves ${\mathcal{O}}_{\mathbb{P}(U)\times \mathbb{P}(V)}(a,b)$ in $D(\mathbb{P}(U\otimes V))$ for $a⩾-\dim (U)$ and $b⩾-\dim (V)$. Also we prove some property of multiplication on syzygy spaces of the Segre embedding.

17 pages, 11 pictures

References in corpus (1)

• Syzygies of Segre embeddings and Delta-modules

Cited by in corpus (1)

• Syzygies of Quadratic Veronese Embedding