Homological projective duality
Publications Mathématiques de l'IHÉS (2007)
- Volume: 105, page 157-220
- ISSN: 0073-8301
Access Full Article
topAbstract
topHow to cite
topReferences
top- 1. A. Bondal, Representations of associative algebras and coherent sheaves (Russian), Izv. Akad. Nauk SSSR, Ser. Mat., 53 (1989), 25-44 Zbl0692.18002MR992977
- 2. A. Bondal and M. Kapranov, Representable functors, Serre functors, and reconstructions (Russian), Izv. Akad. Nauk SSSR, Ser. Mat., 53 (1989), 1183–1205, 1337; translation in Math. USSR-Izv., 35 (1990), 519–541. Zbl0703.14011MR1039961
- 3. A. Bondal and D. Orlov, Semiorthogonal decomposition for algebraic varieties, preprint math.AG/9506012.
- 4. A. Bondal and D. Orlov, Derived categories of coherent sheaves, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), pp. 47–56, Higher Ed. Press, Beijing, 2002. Zbl0996.18007MR1957019
- 5. A. Bondal and D. Orlov, private communication.
- 6. A. Bondal, D. Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compos. Math., 125 (2001), 327-344 Zbl0994.18007MR1818984
- 7. A. Bondal and M. Van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J., 3 (2003), 1–36, 258. Zbl1135.18302MR1996800
- 8. R. Hartshorn, Residues and Duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne., Springer, Berlin, New York (1966) MR222093
- 9. K. Hori and C. Vafa, Mirror Symmetry, arXiv:hep-th/0404196. Zbl1044.14018
- 10. M. Kontsevich, Homological algebra of mirror symmetry, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), pp. 120–139, Birkhäuser, Basel, 1995. Zbl0846.53021MR1403918
- 11. A. Kuznetsov, Hyperplane sections and derived categories (Russian), Izv. Ross. Akad. Nauk, Ser. Mat., 70 (2006), 23-128 Zbl1133.14016MR2238172
- 12. A. Kuznetsov, Derived categories of quadric fibrations and intersections of quadrics, preprint math.AG/0510670.
- 13. A. Kuznetsov, Exceptional collections for Grassmannians of isotropic lines, preprint math.AG/0512013.
- 14. A. Kuznetsov, Homological projective duality for Grassmannians of lines, preprint math.AG/0610957.
- 15. D. Orlov, Projective bundles, monoidal transformations, and derived categories of coherent sheaves (Russian), Izv. Ross. Akad. Nauk, Ser. Mat., 56 (1992), 852-862 Zbl0798.14007MR1208153
- 16. D. Orlov, Equivalences of derived categories and K3 surfaces, algebraic geometry, 7, J. Math. Sci., New York, 84 (1997), 1361-1381 Zbl0938.14019MR1465519
- 17. D. Orlov, Triangulated categories of singularities and D-branes in Landau–Ginzburg models (Russian), Tr. Mat. Inst. Steklova, 246 (2004), 240-262 Zbl1101.81093MR2101296
- 18. D. Orlov, Triangulated categories of singularities and equivalences between Landau–Ginzburg models, preprint math.AG/0503630. Zbl1161.14301