Geometry of projective algebraic curves

TL;DR: In this article, the authors studied smooth rational closed embeddings of the real affine line into the real euclidean plane, that is algebraic rational maps from the real fine line to the real algebraic plane.

TL;DR: In this article, the flow of time is shown to be a part of the objective physical world and the concept of deformation is introduced to explain the three acknowledged properties of time: one-dimensionalality, arrow and flow.

TL;DR: In this paper, a complete classification of the singularities on tame sextics of torus type is given, and it is shown that there exist 121 configurations and there are 5 pairs and a triple of configurations for which the corresponding moduli spaces coincide, ignoring the respective torus decomposition.

TL;DR: In this paper, the authors obtained new examples and the complete list of rational cuspidal plane curves with at least three cusps, one of which has multiplicity δ(C - 2 ).

TL;DR: In this article, a survey on the Ahlfors function and the weaker circle maps is presented, i.e. those (branched) maps effecting the conformal representation upon the disc of a compact bordered Riemann surface.

TL;DR: In this paper, Riemann, Ahlfors, Rohlin, and Rohlin discuss the current consensus about Hilbert's 16th in degree 8, a nearly finished piece of mathematics, thanks to heroic breakthroughs by Viro, Fiedler, Korchagin, Shustin, Chevallier, Orevkov, yet still leaving undecided six tantalizing bosons among a menagerie of 104 logically possible distributions of ovals.