Geodesic
Syzygy Algebras for Segre Embeddings
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 54-74

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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 $\operatorname{GL}(U)\times\operatorname{GL}(V)$ 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 $a\ge-\dim(U)$ and $b\ge-\dim(V)$. We also prove a property of multiplication in syzygy spaces of the Segre embedding.
Keywords: syzygy algebra, representations of $\operatorname{GL}$, Segre embedding, derived category of coherent sheaves.
Mots-clés : Koszul cohomology 
@article{FAA_2013_47_3_a4,
     author = {I. V. Netay},
     title = {Syzygy {Algebras} for {Segre} {Embeddings}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {54--74},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a4/}
}
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I. V. Netay. Syzygy Algebras for Segre Embeddings. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 54-74. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a4/