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
Let k=Q((D 2+md)(D 2+nd)(D 2+rd)), this paper proves firstly that the fundamental unit of k is ε=((D 2+md)(D 2+nd)+D 2(D 2+rd)) 2/(|mn|d 2), where D,d,m,n, and r are rational integers satisfying certain cond...Let k=Q((D 2+md)(D 2+nd)(D 2+rd)), this paper proves firstly that the fundamental unit of k is ε=((D 2+md)(D 2+nd)+D 2(D 2+rd)) 2/(|mn|d 2), where D,d,m,n, and r are rational integers satisfying certain conditions. Consequently, we describe the fundamental unit system of K=Q(D 2+md,D 2+nd,D 2+rd) explicitly by the fundamental unit of all the quadratic subfields and the class number h K explicitly by the class numbers of all the quadratic subfields. We also provide the fundamental unit system of some fields of (2,2) type.展开更多
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.
文摘Let k=Q((D 2+md)(D 2+nd)(D 2+rd)), this paper proves firstly that the fundamental unit of k is ε=((D 2+md)(D 2+nd)+D 2(D 2+rd)) 2/(|mn|d 2), where D,d,m,n, and r are rational integers satisfying certain conditions. Consequently, we describe the fundamental unit system of K=Q(D 2+md,D 2+nd,D 2+rd) explicitly by the fundamental unit of all the quadratic subfields and the class number h K explicitly by the class numbers of all the quadratic subfields. We also provide the fundamental unit system of some fields of (2,2) type.
