Let be a smooth complex projective curve, and let be a vector bundle on which is not semistable. For a suitably chosen integer , let be the Grassmann bundle over that parametrizes the quotients of the fibers of of dimension . Assuming some numerical conditions on the Harder–Narasimhan filtration of , we study Seshadri constants of ample line bundles on . In many cases, we give the precise values of the Seshadri constants. Our results generalize various known results for the special case of . We include some examples in rank .
Soient une courbe projective complexe lisse et un fibré vectoriel sur , supposé non semi-stable. Pour un entier bien choisi, considérons le fibré de Grassman au-dessus de qui paramètre les quotients de dimension des fibrés de . Sous des hypothèses numériques sur la filtration de Harder–Narasimhan de , nous étudions les constantes de Seshadri des fibrés amples au-dessus de . Dans de nombreux cas, nous obtenons les valeurs explicites des constantes de Seshadri. Nos résultats généralisent plusieurs résultats connus dans le cas particulier où . Nous présentons des exemples en rang .
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Accepted:
Published online:
Classification: 14H60, 14Q20, 14C20
Keywords: Seshadri constant, Harder–Narasimhan filtration, Grassmann bundle, nef cone, pseudo-effective cone
Author's affiliations:
@article{AIF_2020__70_4_1477_0, author = {Biswas, Indranil and Hanumanthu, Krishna and Nagaraj, Donihakkalu Shankar and Newstead, Peter E.}, title = {Seshadri constants and {Grassmann} bundles over curves}, journal = {Annales de l'Institut Fourier}, pages = {1477--1496}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {70}, number = {4}, year = {2020}, doi = {10.5802/aif.3370}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3370/} }
TY - JOUR TI - Seshadri constants and Grassmann bundles over curves JO - Annales de l'Institut Fourier PY - 2020 DA - 2020/// SP - 1477 EP - 1496 VL - 70 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3370/ UR - https://doi.org/10.5802/aif.3370 DO - 10.5802/aif.3370 LA - en ID - AIF_2020__70_4_1477_0 ER -
Biswas, Indranil; Hanumanthu, Krishna; Nagaraj, Donihakkalu Shankar; Newstead, Peter E. Seshadri constants and Grassmann bundles over curves. Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1477-1496. doi : 10.5802/aif.3370. https://aif.centre-mersenne.org/articles/10.5802/aif.3370/
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