Exceptional vector bundles on projective spaces

D-branes, exceptional sheaves and quivers on Calabi–Yau manifolds: from Mukai to McKay

“…This is the form in which we expect that the Beilinson complex and Beilinson's theorem to generalize for the more complicated cases under consideration in this paper. We note here that the re-writing of Beilinson's theorem in this language was pointed out by Gorodontsev and Rudakov [31] and also appears for instance in the work of Drézet [32].…”

“…Conjecture 2 (in both forms) is true for P n and seems to follow from the results of Bondal (see Theorem 4.1 in [29]) for spaces with very ample anticanonical class. This implies that there exists a generalisation of Beilinson's theorem [30] for the case of weighted projective spaces along the lines followed by [31,32] for P n . The existence of such a generalisation is also implicit in the work of Douglas and Diaconescu [11].…”

Bundles over Fano threefolds of type V 22

“…We refer to the book [hel90] useful properties of mutations, to [Dre86] and [GR87] for their original use over projective spaces.…”

Derived categories of projective bundles

“…The notion of exceptional collections of sheaves was introduced by Gorodentsev and Rudakov in [7], and we will use strongly exceptional collections of locally free sheaves to construct tilting bundles. Definition 2.1.…”

“…So we are led to pose the following question. Examples of smooth projective varieties with a tilting bundle whose summands are line bundles can be found, for instance, in [6], [7], [9], [13] and [14].…”