Geodesic
Embedding derived categories of Enriques~surfaces in derived categories of Fano varieties
Izvestiya. Mathematics , Tome 83 (2019) no. 3, pp. 534-539.

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that the bounded derived category of coherent sheaves on a general Enriques surface can be realized as a semi-orthogonal component in the derived category of a smooth Fano variety with diagonal Hodge diamond.
Keywords: derived category of coherent sheaves, Fano variety
Mots-clés : Enriques surface. 
@article{IM2_2019_83_3_a5,
     author = {A. G. Kuznetsov},
     title = {Embedding derived categories of {Enriques~surfaces} in derived categories of {Fano} varieties},
     journal = {Izvestiya. Mathematics },
     pages = {534--539},
     publisher = {mathdoc},
     volume = {83},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a5/}
}
TY  - JOUR
AU  - A. G. Kuznetsov
TI  - Embedding derived categories of Enriques~surfaces in derived categories of Fano varieties
JO  - Izvestiya. Mathematics 
PY  - 2019
SP  - 534
EP  - 539
VL  - 83
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a5/
LA  - en
ID  - IM2_2019_83_3_a5
ER  - 
%0 Journal Article
%A A. G. Kuznetsov
%T Embedding derived categories of Enriques~surfaces in derived categories of Fano varieties
%J Izvestiya. Mathematics 
%D 2019
%P 534-539
%V 83
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a5/
%G en
%F IM2_2019_83_3_a5
A. G. Kuznetsov. Embedding derived categories of Enriques~surfaces in derived categories of Fano varieties. Izvestiya. Mathematics , Tome 83 (2019) no. 3, pp. 534-539. http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a5/

[1] S. Galkin, L. Katzarkov, A. Mellit, E. Shinder, Minifolds and phantoms, 2013, arXiv: 1305.4549

[2] A. I. Bondal, A. E. Polishchuk, “Homological properties of associative algebras: the method of helices”, Russian Acad. Sci. Izv. Math., 42:2 (1994), 219–260 | DOI | MR | Zbl

[3] V. Przyjalkowski, C. Shramov, Hodge complexity for weighted complete intersections, 2018, arXiv: 1801.10489

[4] F. R. Cossec, “Reye congruences”, Trans. Amer. Math. Soc., 280:2 (1983), 737–751 | DOI | MR | Zbl

[5] C. Ingalls, A. Kuznetsov, “On nodal Enriques surfaces and quartic double solids”, Math. Ann., 361:1-2 (2015), 107–133 | DOI | MR | Zbl

[6] A. Beauville, Complex algebraic surfaces, Transl. from the French, London Math. Soc. Stud. Texts, 34, 2nd ed., Cambridge Univ. Press, Cambridge, 1996, x+132 pp. | DOI | MR | Zbl

[7] R. Hartshorne, “Ample vector bundles”, Inst. Hautes Études Sci. Publ. Math., 29 (1966), 63–94 | MR | Zbl

[8] A. Kuznetsov, “Homological projective duality”, Publ. Math. Inst. Hautes Études Sci., 105 (2007), 157–220 | DOI | MR | Zbl

[9] D. O. Orlov, “Triangulated categories of singularities and equivalences between Landau–Ginzburg models”, Sb. Math., 197:12 (2006), 1827–1840 | DOI | DOI | MR | Zbl

[10] M. Bernardara, M. Bolognesi, D. Faenzi, “Homological projective duality for determinantal varieties”, Adv. Math., 296 (2016), 181–209 | DOI | MR | Zbl

[11] Young-Hoon Kiem, In-Kyun Kim, Hwayoung Lee, Kyoung-Seog Lee, “All complete intersection varieties are Fano visitors”, Adv. Math., 311 (2017), 649–661 | DOI | MR | Zbl

[12] Young-Hoon Kiem, Kyoung-Seog Lee, Fano visitors, Fano dimension and orbifold Fano hosts, 2015, arXiv: 1504.07810

[13] M. S. Narasimhan, “Derived categories of moduli spaces of vector bundles on curves”, J. Geom. Phys., 122 (2017), 53–58 | DOI | MR | Zbl

[14] A. Fonarev, A. Kuznetsov, “Derived categories of curves as components of Fano manifolds”, J. Lond. Math. Soc. (2), 97:1 (2018), 24–46 | DOI | MR | Zbl