Email this article On the derived category of $\mathrm{IGr}(3,8)$
- Authors: Guseva L.A.1
-
Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 211, No 7 (2020)
- Pages: 24-59
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133334
- DOI: https://doi.org/10.4213/sm9292
- ID: 133334
Cite item
Open Access
Access granted
Subscription Access
Abstract
We construct a full exceptional collection of vector bundles in the bounded derived category of coherent sheaves on the Grassmannian $\mathrm{IGr}(3,8)$ of isotropic 3-dimensional subspaces in a symplectic vector space of dimension 8.Bibliography: 16 titles.
About the authors
Lyalya Andreevna Guseva
Steklov Mathematical Institute of Russian Academy of Sciences
Email: lguseva@hse.ru
References
- А. А. Бейлинсон, “Когерентные пучки на $mathbf P^n$ и проблемы линейной алгебры”, Функц. анализ и его прил., 12:3 (1978), 68–69
- А. И. Бондал, “Представления ассоциативных алгебр и когерентные пучки”, Изв. АН СССР. Сер. матем., 53:1 (1989), 25–44
- M. Demazure, “A very simple proof of Bott's theorem”, Invent. Math., 33:3 (1976), 271–272
- D. Faenzi, L. Manivel, “On the derived category of the Cayley plane II”, Proc. Amer. Math. Soc., 143:3 (2015), 1057–1074
- А. В. Фонарëв, “Минимальные лефшецевы разложения производных категорий грассманианов”, Изв. РАН. Сер. матем., 77:5 (2013), 203–224
- M. M. Kapranov, “On the derived categories of coherent sheaves on some homogeneous spaces”, Invent. Math., 92:3 (1988), 479–508
- А. Г. Кузнецов, “Гиперплоские сечения и производные категории”, Изв. РАН. Сер. матем., 70:3 (2006), 23–128
- A. Kuznetsov, “Homological projective duality”, Publ. Math. Inst. Hautes Etudes Sci., 105 (2007), 157–220
- A. Kuznetsov, “Exceptional collections for Grassmannians of isotropic lines”, Proc. Lond. Math. Soc. (3), 97:1 (2008), 155–182
- A. Kuznetsov, “Calabi–Yau and fractional Calabi–Yau categories”, J. Reine Angew. Math., 2019:753 (2019), 239–267
- A. Kuznetsov, A. Polishchuk, “Exceptional collections on isotropic Grassmannians”, J. Eur. Math. Soc. (JEMS), 18:3 (2016), 507–574
- A. Kuznetsov, M. Smirnov, “On residual categories for Grassmannians”, Proc. Lond. Math. Soc. (3), 120:5 (2020), 617–641
- Д. О. Орлов, “Проективные расслоения, моноидальные преобразования и производные категории когерентных пучков”, Изв. РАН. Сер. матем., 56:4 (1992), 852–862
- A. Polishchuk, A. Samokhin, “Full exceptional collections on the Lagrangian Grassmannians $LG(4,8)$ and $LG(5,10)$”, J. Geom. Phys., 61:10 (2011), 1996–2014
- А. В. Самохин, “Производная категория когерентных пучков на $LG_3^{mathbf C}$”, УМН, 56:3(339) (2001), 177–178
- J. Weyman, Cohomology of vector bundles and syzygies, Cambridge Tracts in Math., 149, Cambridge Univ. Press, Cambridge, 2003, xiv+371 pp.
Supplementary files
