1 - 10 of 12 articles
We study the relationship between the tight closure of an ideal and the sum of all ideals in its linkage class
We present a new simple proof of the famous theorem of Abhyankar, Moh and Suzuki about rational curves in a plane. This proof relies on the Poincaré–Hopf theorem.
We establish a weak form of Carlson's conjecture on the depth of the mod-p cohomology ring of a p-group. In particular, Duflot's lower bound for the depth is tight if and only if the cohomology ring is not detected on a certain family of subgroups. The proofs use the structure of the cohomology...
We prove that solutions for ¯∂ get 1/M-derivatives more than the data in L
-Sobolev spaces on a bounded convex domain of finite type M by means of the integral kernel method. Also we prove that the Bergman projection is invariant under the L
-Sobolev spaces of fractional orders by different...
In this paper we study removable singularities for holomorphic functions such that sup
<∞. Spaces of this type include spaces of holomorphic functions in Campanato classes, BMO and locally Lipschitz classes. Dolzhenko (1963), Král (1976) and Nguyen (1979)...
Differential equations are derived for a continous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
Demushkin's Theorem says that any two toric structures on an affine variety X are conjugate in the automorphism group of X. We provide the following extension: Let an (n−1)-dimensional torus T act effectively on an n-dimensional affine toric variety X. Then T is conjugate in the automorphism...
Suppose that G is a group scheme which is finite and étale over a Noetherian scheme S. The main result of this paper asserts the existence of a bijection between the sets of isomorphism classes of qfh and étale torsors over S with coefficients in G.
Extending results for space curves we establish bounds for the cohomology of a non-degenerate curve in projective $n$-space. As a consequence, for any given $n$ we determine all possible pairs $(d, g)$ where $d$ is the degree and $g$ is the (arithmetic) genus of the curve. Furthermore, we show...
We determine all complete intersection surface germs whose Pythagoras number is 2, and find that they are all embedded in ℝ3 and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function germs. In addition, we discuss completely these...
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