We show that the arithmetically Cohen–Macaulay (ACM) curves of degree 4 and genus 0 in P 4 form an irreducible subset of the Hilbert scheme. Using this, we show that the singular locus of the corresponding component of the Hilbert scheme has dimension greater than 6. Moreover, we describe the structures of all ACM curves of Hilb 4m+1 (P 4).

Let p be a canonically associative, multiplicative, separable subset. We wish to extend the results of [5] to totally super-admissible, Eratosthenes, canonical paths. We show that ‖G‖ 6 = |F |. A central problem in local logic is the description of partially irreducible scalars. The groundbreaking work of W. Cardano on planes was a major advance.

We prove that the restriction of a probability measure invariant under a nonhyperbolic, ergodic and totally irreducible automorphism of a compact connected abelian group to the leaves of the central foliation is severely restricted. We also prove a topological analogue of this result: the intersection of every proper closed invariant subset with each central leaf is compact.

A primitive multiple scheme is a Cohen-Macaulay $Y$ such that the associated reduced $X=Y_{red}$ smooth, irreducible, and can be locally embedded in smooth variety of dimension $\dim(X)+1$. If $n$ multiplicity $Y$, there canonical filtration $X=X_1\subset X_2\subset\cdots\subset X_n=Y$, $X_i$ $i$. The simplest example trivial to line bundle $L$ on $X$: it $n$-th infinitesimal neighborhood $X$, ...

In this paper, we study the approximability of the capacitated network design problem (Cap-NDP) on undirected graphs: GivenG = (V,E) with non-negative costs c and capacities u on its edges, sourcesink pairs (si, ti) with demand ri, the goal is to find the minimum cost subgraph where the minimum (si, ti) cut with u-capacities is at least ri. When u ≡ 1, we get usual SNDP for which Jain gave a 2-...

On the torus of dimension 2, 3, or 4, we show that the subset of diffeomorphisms with trivial centralizer in the C topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.

The group algebra of the symmetric group and properties of the irreducible characters are used to derive combinatorial properties of embeddings of rooted maps in orientable surfaces of arbitrary genus. In particular, we show that there exists, for each genus, a correspondence between the set of rooted quadrangulations and a set of rooted maps of all lower genera with a distinguished subset of v...

Let $X/\mathbb {F}_{q}$ be a smooth, geometrically connected, quasi-projective scheme. $\mathcal {E}$ semi-simple overconvergent $F$ -isocrystal on $X$ . Suppose that irreducible summands {E}_i$ of have rank 2, determinant $\bar {\mathbb {Q}}_p(-1)$ , and infinite monodromy at $\infty$ further for each closed point $x$ the characteristic polynomial is in $\mathbb {Q}[t]\subset \mathbb {Q}_p[t]$...

A primitive multiple scheme is a Cohen–Macaulay Y such that the associated reduced $$X=Y_{\mathrm{red}}$$ smooth, irreducible, and can be locally embedded in smooth variety of dimension $$\dim (X)+1$$ . If n multiplicity Y, there canonical filtration $$X=X_1\subset X_2\subset \cdots \subset X_n=Y$$ , $$X_i$$ i. The simplest example trivial to line bundle L on X: it nth infinitesimal neighborhoo...

Let $R$ be a commutative ring with identity and $M$ be an$R$-module. Let $FSpec(M)$ denotes the collection of all prime fuzzysubmodules of $M$. In this regards some basic properties of Zariskitopology on $FSpec(M)$ are investigated. In particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$FSpec(M)$ is a $T_0-$spa...