Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664512003Multiple Structures on P<sup>1</sup>: Rational Ropes ENEdoardoBallico<p>Here we study the theory of rational ropes (multiple structures on P<sup>1</sup> whose ideal sheaf, F, has square zero) introduced by K. Chandler. F is a vector bundle on P<sup>1</sup> and here we show that several
properties of the rope depend on the splitting type of F. We study the moduli space of all rational ropes with F as ideal sheaf.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Real Embeddings of Real Projective Curves and Real Ramification Points ENEdoardoBallico<p>Here we study real immersions in a projective space of
smooth projective curves defined over R but without real ramification points, giving several examples for canonical embeddings (i.e. existence of real curves without real Weierstrass points) and for plane curves. We also gives numerical obstructions to the existence of real morphisms
without real ramification points.</p>
No potential conflict of interest relevant to this article was reported.