An arithmetic theory of adjoint plane curves

Abstract

Pi. In this case, the degree of the fixed component is 23<_i r<(f<-1), while the number of conditions which the adjoint curves impose on the curves of sufficiently high degree is zZ'i^nin-D/l.

The Briançon-Skoda number of analytic irreducible planar curves

“…We conclude by Lemma 2.1 and (2.8) that bs(C) is the smallest integer that is strictly larger than c/m+1−1/m, which is the same as 1+c/m . Gorenstein [7] and Samuel [17] (see Kodaira [11,10] for corresponding result in the analytic setting) prove that c = 2δ, where δ is a well-known invariant in singularity theory. Finally, by Theorem 10.5 in [15], µ = 2δ.…”

Adjoints and Max Noether’s Fundamentalsatz

“…is known as Gorenstein's theorem [8]. It depends on the fact that C is a curve on a nonsingular surface.…”

“…The treatments we have found in the literature are either computationally difficult ( [8], [14]), or involve quite a bit of advanced machinery: at least the machinery of sheaves and cohomology ( [16]), or even residues and duality ( [10]). See Serre [15], Chap.…”

Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes

“…A n are exactly those in the complete linear system |Kχ + (n − m + 3) L|, Kχ a canonical divisor onχ, L the hyperplane section divisor and m = deg χ (see [11] for details).…”