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Article

Алгебры сизигий вложений Сегре

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