As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric or...As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on R^n. In this paper we investigate and reprove some of Kawamata＇s results from this perspective.展开更多
We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducib...We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane(ramified at a smooth sextic curve) that contains 8,910 smooth conics.展开更多
文摘As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on R^n. In this paper we investigate and reprove some of Kawamata＇s results from this perspective.
文摘We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane(ramified at a smooth sextic curve) that contains 8,910 smooth conics.
