Related papers: On Strong Lefschetz Property of 0-dimensional comp…

For a given pair of maps f,g:X->M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism L:H(X)->H(M) of degree (-n). We prove a Lefschetz-type coincidence theorem: if the Lefschetz…

We give a necessary and sufficient condition for a standard graded Artinian ring defined by an m-full ideal, to have the weak Lefschetz property in terms of graded Betti numbers. This is a generalization of a theorem of Wiebe for…

Let $X$ be a (real or complex) infinite dimensional linear space. We establish conditions on a homogeneous polynomial $P$ on $X$ so that, if $W$ is any finite dimensional subspace of $X$ on which $P$ vanishes, then $P$ vanishes on an…

We study three classes of local homomorphisms and their behavior with respect to the ascent and descent of the \emph{complete intersection} property. Crucially, they fall in between the already studied classes of complete intersection and…

Codimension two Artinian algebras $A$ have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three AG algebras -…

We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal…

We provide a description of initial ideals for almost complete intersections generated by powers of general linear forms and prove that WLP in a fixed degree $d$ holds when the number of variables $n$ is sufficiently large compared to $d$.…

We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3), \hspace{1pt} \mathrm{SO}(5,\mathbb{C})/\mathrm{SO}(5),$ and…

For a wide class of Dirichlet series associated to automorphic forms, we show that those without Euler products must have zeros within the region of absolute convergence. For instance, we prove that if f is a classical holomorphic modular…

Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian pairing on this space with values in the complex vector space…

We prove that the $d$-component of the generic initial ideal, with respect to the reverse lexicographic order, of an ideal generated by a regular sequence of homogeneous polynomials of degree $d$ is revlex in a particular, but important,…

We study the weak Lefschetz property and the Hilbert function of level Artinian monomial almost complete intersections in three variables. Several such families are shown to have the weak Lefschetz property if the characteristic of the base…

Using aritmethic conditions on affine semigroups we prove that for a simplicial toric variety of codimension 2 the property of being a set-theoretic complete intersection on binomials in characteristic $p$ holds either for all primes $p$,…

Let $I$ be ideal of an $n$-dimensional local Gorenstein ring $R$. In this paper we will describe several necessary and sufficient conditions such that the ideal $I$ becomes cohomologically complete intersections. In fact, as a technical…

We say that a (∨,0)-semilattice S is conditionally co-Brouwerian, if (1) for all nonempty subsets X and Y of S such that X $\leq$ Y (i.e., x $\leq$ y for all (x, y) $\in$ X x Y), there exists z $\in$ S such that X $\leq$ z $\leq$ Y,…

Consider $L$ a regular Lagrangian, $S$ the canonical semispray, and $h$ the horizontal projector of the canonical nonlinear connection. We prove that if the Lagrangian is constant along the integral curves of the Euler-Lagrange equations…

We consider the nonlocal Cahn-Hilliard equation with singular (logarithmic) potential and constant mobility in three-dimensional bounded domains and we establish the validity of the instantaneous strict separation property. This means that…

A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we prove that if G is a group with the property that every closed subgroup of G is locally pseudocompact, then G_0 is…

We compute the generic initial ideal of a complete intersection of embedding dimension three with strong Lefschetz property and we show that it is an almost reverse lexicographic ideal. This enable us to give a proof for Moreno's conjecture…

Let $(X,d,m)$ be a geodesic metric measure space. Consider a geodesic $\mu_{t}$ in the $L^{2}$-Wasserstein space. Then as $s$ goes to $t$ the support of $\mu_{s}$ and the support of $\mu_{t}$ have to overlap, provided an upper bound on the…