Related papers: Segre powers of posets preserve EL-shellability
The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of…
We prove the equivalence of EL-shellability and the existence of recursive atom ordering independent of roots. We show that a comodernistic lattice, as defined by Schweig and Woodroofe, admits a recursive atom ordering independent of roots,…
A Schubert variety in the complete flag manifold $GL_n/B$ is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give a combinatorial classification of these Schubert varieties.…
We investigate the partial orderings of the form (P(X),\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures and show that if the components of X are maximally…
We prove the Trung's conjecture about Segre's upper bound for s equimultiple fat points not on a linear (r-1)-space, s\le r+3, by algebraic method used in [3]. This method also may used to research other cases of fat points.
The paper is devoted to a detailed study of sextics in three variables having a decomposition as a sum of nine powers of linear forms. This is the unique case of a Veronese image of the plane which, in the terminology introduced by…
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric…
Generalizing a variety of earlier problems on stable contracts in two-sided markets, Alkan and Gale introduced in 2003 a general stability model on a bipartite graph $G=(V,E)$ in which the vertices are interpreted as ``agents'', and the…
Let $\{C_i : i=1,\ldots,r\}$ be a set of irreducible plane curve singularities. For an action of a finite group $G$, let $\Delta^{L}(\{t_{a i}\})$ be the Alexander polynomial in $r\vert G\vert$ variables of the algebraic link…
Following a recent work in which it is shown that a spacetime admitting Lie-group actions may be disjointly decomposed into a a closed subset with no interior plus a dense finite union of open sets in each of which the character and…
In a letter to Tate, Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions on an adelic double coset space constructed from the endomorphism algebra of…
In a letter to Tate (published in Israel J. Math. in 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions on an adelic double coset space…
Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $\theta$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_\theta(G) \subseteq V$ of semistable points. We give necessary,…
The Iwasawa $\mu$-invariant of the Selmer group of a residually reducible Galois representation arising from a Hecke eigencuspform is studied. Furthermore, certain Iwasawa-invariants refining the $\mu$-invariant are defined and analyzed. As…
Some posets of binary leaf-labeled trees are shown to be supersolvable lattices and explicit EL-labelings are given. Their characteristic polynomials are computed, recovering their known factorization in a different way.
We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincare polynomials of the…
We propose a generalization of SHGH Conjectures to a smooth projective surface Y: the so called Segre Problem. The study of linear systems on Y can be translated in terms of the Mori cone of the blow up $X = Bl_r Y$ at $r$ general points.…
Elastic scattering amplitudes dominated by the Pomeron singularity which obey the principal unitarity bounds at high energies are constructed and analyzed. Confronting the models of double and triple (at $t=0$) Pomeron pole (supplemented by…
We reformulate the persistent (co)homology of simplicial filtrations, viewed from a more algebraic setting, namely as the (co)homology of a chain complex of graded modules over polynomial ring $K[t]$. We also define persistent (co)homology…
Segre surfaces in the title mean quartic surfaces in $\mathbb{CP}^4$ which are the images of weak del Pezzo surfaces of degree four under the anti-canonical map. We first show that minimal minitwistor spaces with genus one are exactly Segre…