Uniform Steiner bundles

Marchesi, Simone; Miró-Roig, Rosa Maria

Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 447-472.

Dans ce travail, nous étudions les fibrés uniformes de Steiner de type $k$, ou $k$ est le degré le plus bas de la décomposition. Nous prouvons des limites supérieures et inférieures strictes pour le rang dans le cas $k=1$ et, de plus, nous donnons des familles d’exemples pour chaque rang possible et nous expliquons quelle relation existe entre les familles. Après avoir traité le cas $k$ en général, nous conjecturons que chaque fibré uniforme de Steiner de type $k$ est obtenu par la technique de construction proposée.

In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case $k=1$ and moreover we give families of examples for every allowed possible rank and explain which relation exists between the families. After dealing with the case $k$ in general, we conjecture that every $k$-type uniform Steiner bundle is obtained through the proposed construction technique.

Classification : 14F05, 14J60
Keywords: Uniform bundles, Steiner bundles
Mot clés : Fibrés de Steiner, Fibrés uniformes

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