Dual exceptional collections on Lagrangian Grassmannians
Sbornik. Mathematics, Tome 214 (2023) no. 12, pp. 1779-1800 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We construct graded left dual exceptional collections to the exceptional collections generating the Kuznetsov-Polishchuk blocks on Lagrangian Grassmannians. As an application, we find explicit resolutions for some natural irreducible equivariant vector bundles. Bibliography: 13 titles.
Keywords: derived categories, Grassmannians.
Mots-clés : exceptional collections
@article{SM_2023_214_12_a5,
     author = {A. V. Fonarev},
     title = {Dual exceptional collections on {Lagrangian} {Grassmannians}},
     journal = {Sbornik. Mathematics},
     pages = {1779--1800},
     year = {2023},
     volume = {214},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2023_214_12_a5/}
}
TY  - JOUR
AU  - A. V. Fonarev
TI  - Dual exceptional collections on Lagrangian Grassmannians
JO  - Sbornik. Mathematics
PY  - 2023
SP  - 1779
EP  - 1800
VL  - 214
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2023_214_12_a5/
LA  - en
ID  - SM_2023_214_12_a5
ER  - 
%0 Journal Article
%A A. V. Fonarev
%T Dual exceptional collections on Lagrangian Grassmannians
%J Sbornik. Mathematics
%D 2023
%P 1779-1800
%V 214
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2023_214_12_a5/
%G en
%F SM_2023_214_12_a5
A. V. Fonarev. Dual exceptional collections on Lagrangian Grassmannians. Sbornik. Mathematics, Tome 214 (2023) no. 12, pp. 1779-1800. http://geodesic.mathdoc.fr/item/SM_2023_214_12_a5/

[1] A. Beilinson, “Coherent sheaves on $\mathbf P^n$ and problems of linear algebra”, Funct. Anal. Appl., 12:3 (1978), 214–216 | DOI | MR | Zbl

[2] A. I. Bondal, “A symplectic groupoid of triangular bilinear forms and the braid group”, Izv. Math., 68:4 (2004), 659–708 | DOI | DOI | MR | Zbl

[3] M. M. Kapranov, “On the derived category of coherent sheaves on Grassmann manifolds”, Math. USSR-Izv., 24:1 (1985), 183–192 | DOI | MR | Zbl

[4] M. M. Kapranov, “On the derived categories of coherent sheaves on some homogeneous spaces”, Invent. Math., 92:3 (1988), 479–508 | DOI | MR | Zbl

[5] A. Kuznetsov, “Exceptional collections for Grassmannians of isotropic lines”, Proc. Lond. Math. Soc. (3), 97:1 (2008), 155–182 | DOI | MR | Zbl

[6] A. Kuznetsov and M. Smirnov, “Residual categories for (co)adjoint Grassmannians in classical types”, Compos. Math., 157:6 (2021), 1172–1206 | DOI | MR | Zbl

[7] A. Kuznetsov and A. Polishchuk, “Exceptional collections on isotropic Grassmannians”, J. Eur. Math. Soc. (JEMS), 18:3 (2016), 507–574 | DOI | MR | Zbl

[8] A. I. Bondal, “Representation of associative algebras and coherent sheaves”, Math. USSR-Izv., 34:1 (1990), 23–42 | DOI | MR | Zbl

[9] A. I. Bondal and M. M. Kapranov, “Representable functors, Serre functors, and mutations”, Math. USSR-Izv., 35:3 (1990), 519–541 | DOI | MR | Zbl

[10] A. L. Gorodentsev and S. A. Kuleshov, “Helix theory”, Mosc. Math. J., 4:2 (2004), 377–440 | DOI | MR | Zbl

[11] A. Fonarev, “Full exceptional collections on Lagrangian Grassmannians”, Int. Math. Res. Not. IMRN, 2022:2 (2022), 1081–1122 | DOI | MR | Zbl

[12] Kyoung-Seog Lee and Kyeong-Dong Park, “Moduli spaces of Ulrich bundles on the Fano 3-fold $V_5$”, J. Algebra, 574 (2021), 262–277 | DOI | MR | Zbl

[13] J. Weyman, Cohomology of vector bundles and syzygies, Cambridge Tracts in Math., 149, Cambridge Univ. Press, Cambridge, 2003, xiv+371 pp. | DOI | MR | Zbl