Smooth ponts of p-adic subanalytic sets.
In a recent paper, Gallego, González and Purnaprajna showed that rational 3-ropes can be smoothed. We generalise their proof, and obtain smoothability of rational m-ropes for m ≥ 3.
Define for a smooth compact hypersurface of its crumpleness as the ratio , where is the distance from to its central set. (In other words, is the maximal radius of an open non-selfintersecting tube around in We prove that any -dimensional non-singular compact algebraic hypersurface of degree is rigidly isotopic to an algebraic hypersurface of degree and of crumpleness . Here , depend only on , and rigid isotopy means an isotopy passing only through hypersurfaces of degree...
Soient un corps commutatif et un idéal de l’anneau des polynômes (éventuellement ). Nous prouvons une conjecture de C. Berenstein - A. Yger qui affirme que pour tout polynôme , élément de la clôture intégrale de l’idéal , on a une représentationoù .