Let Z ⊂ P, r ≥ 4, be a closed subscheme with dim(Z) ≤ r−4. Fix integers c > 0 and gi ≥ 0, i = 1, . . . , c. We prove that the general union of Z and c smooth curves Yi ⊂ P with genus gi and deg(Yi) ≥ r + gr as maximal rank (i.e. the expected postulation) if deg(Y1) + · · ·+ deg(Yc) 0.

We investigate operators which take a set X to a set relatively computably enumerable in and above X by studying which such sets X can be so mapped into the Turing degree of K. We introduce notions of nontriviality for such operators, and use these to study which additional properties can be required of sets which can be completed to the jump by given c.e. operators.

For a positive integer k, a k-subdominating function of a graph G=(V; E) is a function f :V →{−1; 1} such that ∑u∈NG [v] f(u)¿ 1 for at least k vertices v of G. The ksubdomination number of G, denoted by ks(G), is the minimum of ∑ v∈V f(v) taken over all k-subdominating functions f of G. In this article, we prove a conjecture for k-subdomination on trees proposed by Cockayne and Mynhardt. We al...

We show that the identity bounded Turing degrees of computably enumerable sets are not dense.

in this paper, the notion of fuzzy semicompactness degrees isintroduced in $l$-fuzzy topological spaces by means of theimplication operation of $l$. characterizations of fuzzysemicompactness degrees in $l$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

For reducibilities r and r′ such that r is weaker than r′, we say that the r-degree of A, i.e., the class of sets which are r-equivalent to A, collapses to the r′-degree of A if both degrees coincide. We investigate for the polynomial-time bounded many-one, bounded truth-table, truth-table, and Turing reducibilities whether and under which conditions such collapses can occur. While we show that...

We work throughout over the complex numbers C, i.e. all schemes are over C and all maps of schemes are maps of C-schemes. A curve, unless otherwise stated, is a smooth complete curve. Points mean geometric points. We will, as is usual in such situations, toggle between the algebraic and analytic categories without warning. For a curve X , SUX(n, L) will denote the moduli space of semi-stable ve...

Computing Delaunay triangulations in R involves evaluating the so-called in_sphere predicate that determines if a point x lies inside, on or outside the sphere circumscribing d+ 1 points p0, . . . , pd. This predicate reduces to evaluating the sign of a multivariate polynomial of degree d + 2 in the coordinates of the points x, p0, . . . , pd. Despite much progress on exact geometric computing,...