Consider a smooth complex surface $X$ which is double cover of the projective plane $\mathbb{P}^2$ branched along curve degree $2s$. In this article, we study geometric conditions are equivalent to existence Ulrich line bundles on with respect covering. Also, for every $s\geq 1$, describe classes such surfaces admit and give examples.

The long standing Lech’s conjecture in commutative algebra states that for a flat local extension $$(R,\mathfrak {m})\rightarrow (S,\mathfrak {n})$$ of Noetherian rings, we have an inequality on the Hilbert–Samuel multiplicities: $$e(R)\le e(S)$$ . In general is wide open when $$\dim R>3$$ , even equal characteristic. this paper, prove all dimensions, provided {m})$$ standard graded ring over p...

Ulrich Wagner (Hg.): Geschichte der Stadt Würzburg. Bd. III: Vom Übergang an Bayern 1814 bis zum 21. Jahrhundert. Stuttgart (Konrad Theiss) 2007. 2 Teilbde.: 1586 S., 76 Farbtafeln, 538 Textabb.

Rolf-Ulrich Kunze, Lehrbuch Familiengeschichte. Eine Ressource der Zeitgeschichte, Stuttgart: Kohlhammer 2018. 232 S., 13 Abb. ISBN 978-3-17-033929-3. € 29,–

We construct a steady analytic accretion flow model for a finite rotating gas cloud that accretes material to a central gravitational object. The pressure gradients of the flow are considered to be negligible and so, the flow is ballistic. We also assume a steady flow and consider the particles at the boundary of the spherical cloud to be rotating as a rigid body, with a fixed amount of inwards...