Homological projective duality

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A. Bondal and D. Orlov, Semiorthogonal decomposition for algebraic varieties, preprint math.AG/9506012.

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.

A. Bondal and D. Orlov, private communication.

A. Bondal and D. Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compos. Math., 125 (2001), 327–344.

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.

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. Lect. Notes Math., 20, Springer, Berlin, New York, 1966.

K. Hori and C. Vafa, Mirror Symmetry, arXiv:hep-th/0404196.

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.

A. Kuznetsov, Hyperplane sections and derived categories (Russian), Izv. Ross. Akad. Nauk, Ser. Mat., 70 (2006), 23–128.

A. Kuznetsov, Derived categories of quadric fibrations and intersections of quadrics, preprint math.AG/0510670.

A. Kuznetsov, Exceptional collections for Grassmannians of isotropic lines, preprint math.AG/0512013.

A. Kuznetsov, Homological projective duality for Grassmannians of lines, preprint math.AG/0610957.

D. Orlov, Projective bundles, monoidal transformations, and derived categories of coherent sheaves (Russian), Izv. Ross. Akad. Nauk, Ser. Mat., 56 (1992), 852–862; translation in Russ. Acad. Sci., Izv., Math., 41 (1993), 133–141.

D. Orlov, Equivalences of derived categories and K3 surfaces, algebraic geometry, 7, J. Math. Sci., New York, 84 (1997), 1361–1381.

D. Orlov, Triangulated categories of singularities and D-branes in Landau–Ginzburg models (Russian), Tr. Mat. Inst. Steklova, 246 (2004), 240–262; translation in Proc. Steklov Inst. Math., 246 (2004), 227–248.

D. Orlov, Triangulated categories of singularities and equivalences between Landau–Ginzburg models, preprint math.AG/0503630.