Search results for "Kummer surface"

On the signature of four-manifolds with universal covering spin

1993

In this note we study closed oriented 4-manifolds whose universal covering is spin and ask whether there are restrictions on the divisibility of the signature. Since any natural number appears as the signature of a connected sum of r 2,s, without the assumption on the universal covering there cannot exist any restrictions. Certainly, the most famous such restriction was proved by Rohlin in [10], where he showed that the signature a of a smooth 4-dimensional spin manifold is divisible by 16 (compare part (2) of our Main Theorem for a new proof). The Kummer surface K shows that this is the best possible general result. Dividing by a certain free holomorphic involution on K, one obtains the En…

Some closed 4-manifolds with exotic differentiable structure

1984

Transcendental lattices of some K 3-surfaces

2008

In a previous paper, (S2), we described six families of K3-surfaces with Picard- number 19, and we identified surfaces with Picard-number 20. In these notes we classify some of the surfaces by computing their transcendental lattices. Moreover we show that the surfaces with Picard-number 19 are birational to a Kummer surface which is the quotient of a non-product type abelian surface by an involution.

Models as Research Tools: Plücker, Klein, and Kummer Surfaces

2018

In the late summer of 1869, 20-year-old Felix Klein made his way to Berlin, where he planned to attend the renowned seminar founded by Ernst Eduard Kummer and Karl Weierstrass. Klein had already taken his doctorate in Bonn and he would soon be recognized as a leading expert on line geometry, a new approach to 3-space launched by his mentor in Bonn, Julius Plucker. Just before Plucker died in 1868, he entrusted Klein to complete the classic monograph, Neue Geometrie des Raumes gegrundet auf die Betrachtung der geraden Linie als Raumelement. Overall responsibility for this project fell to Alfred Clebsch in Gottingen, which was how Klein first came to the prestigious Georgia Augusta. There he …