Year: 2011
Type: preprint
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 ${\rm GL}(U)\times {\rm GL}(V)$ and construct the minimal resolutions of the sheaves $\mathscr{O}_{\mathbb{P}(U)\times\mathbb{P}(V)}(a,b)$ in $D(\mathbb{P}(U\otimes V))$ for $a\geqslant-\dim(U)$ and $b\geqslant-\dim(V)$. Also we prove some property of multiplication on syzygy spaces of the Segre embedding.
Source: arXiv (Cornell University)
Author: Netay, Igor V.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G4084595387, G8403477372
OpenAlex ID: W2949909658