Mukai flops and derived categories
| dc.creator | Namikawa, Yoshinori | |
| dc.date | 2002-03-28 | |
| dc.date | 2002-06-05 | |
| dc.date.accessioned | 2026-07-07T06:32:53Z | |
| dc.date.available | 2026-07-07T06:32:53Z | |
| dc.description | In this note, we shall prove that two smooth projective varieties of dim 2n connected by a Mukai flop have equivalent bounded derived categories. More precisely, let $ϕ: X - - \to X^+$ be a Mukai flop with centers $Y \subset X$ and $Y^+ \subset X^+$. In our case, the natural fuctor $Φ: D(X) \to D(X^+)$ defined by the graph of $ϕ$ is not fully faithful. Instead, let $X \to {\bar X}$ and $X^+ \to {\bar X}$ be the birational contraction maps of the centers, and put ${\hat X} := X \times_{{\bar X} X^+$. Then ${\hat X}$ is a normal crossing variety with two irreducible components. This ${\hat X}$ defines a functor $Ψ: D(X) \to D(X^+)$. We shall prove that this $Ψ$ is an equivalence. Recently, Wierzba and Wisniewski have announced that two birationally equivalent, complex projective symplectic 4-folds are connected by a finite sequence of Mukai flops. Our result with this shows that $D(X)$ is a birational invariant for complex projective symplectic 4-folds. | |
| dc.description | revised version | |
| dc.identifier | https://arxiv.org/abs/math/0203287 | |
| dc.identifier | http://arxiv.org/abs/math/0203287 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99010 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Mukai flops and derived categories | |
| dc.type | text |