Related papers: Syzygies of Segre embeddings and Delta-modules

It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle $E_{d_1,..., d_n}$ on $\PP^N$ defined as the kernel of a general epimorphism $\xymatrix{\phi:\cO(-d_1)\oplus...\oplus\cO(-d_n)\ar[r] &\cO}$ is…

We define a simple, explicit map sending a morphism $f:M \rightarrow N$ of pointwise finite dimensional persistence modules to a matching between the barcodes of $M$ and $N$. Our main result is that, in a precise sense, the quality of this…

We describe the $p$-divisibility transposition for the Fourier coefficients of Hermitian modular forms. The results show that the same phenomenon as that for Siegel modular forms holds for Hermitian modular forms.

We review the author's results on Mather's $\beta$ function : non-strict convexity of $\beta$ when the configuration space has dimension two, link between the size of the Aubry set and the differentiability of $\beta$, correlation between…

We concern the VIGRE's conjecture; namely the complexity of a Specht module is the p-weight of the corresponding partition if and only if the partition is not p by p. In abelian defect case, we calculate the cohomological variety of the…

A "folklore conjecture, probably due to Tutte" (as described in [P.D. Seymour, Sums of circuits, Graph theory and related topics (Proc. Conf., Univ. Waterloo, 1977), pp. 341-355, Academic Press, 1979]) asserts that every bridgeless cubic…

FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the…

We consider the Segre embedding of the product $\mathbb{C}P^p\times\mathbb{C}P^q$ into $\mathbb{C}P^{p+q+pq}$ and study the biharmonicity of $M^p\times\mathbb{C}P^q$ and $M^p_1\times M^q_2$ as submanifolds of $\mathbb{C}P^{p+q+pq}$, where…

This research presents the results of a study on the existence and frequency distribution of the shell primes defined herein as prime numbers that result from the calculation of the "half-shell" of an p-dimensional entity of the form…

In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebras with square roots focusing on their new characterizations.…

Let $p$ be an odd prime. Denote a Sylow $p$-subgroup of $GL_2(\mathbb{Z}/p^n)$ and $SL_2(\mathbb{Z}/p^n)$ by $S_p(n,GL)$ and $S_p(n,SL)$ respectively. The theory of stable elements tells us that the mod-$p$ cohomology of a finite group is…

The aim of this paper is to construct certain closed embeddings of Grassmannian varieties, using tensor operations on vector bundles. These embeddings generalize Segre and Pl\"ucker morphisms.

Sequence transformations are valuable numerical tools that have been used with considerable success for the acceleration of convergence and the summation of diverging series. However, our understanding of their theoretical properties is far…

Let $p$ be any odd prime number. Let $k$ be any positive integer such that $2\leq k\leq [\frac{p+1}3]+1$. Let $S = (a_1,a_2,...,a_{2p-k})$ be any sequence in ${\Bbb Z}_p$ such that there is no subsequence of length $p$ of $S$ whose sum is…

Let $S=\langle d_1,\dots,d_m\rangle$ be a numerical semigroup and $k[S]$ its semigroup ring. The Hilbert numerator of $k[S]$ determines normalized alternating syzygy power sums $K_p(S)$ encoding alternating power sums of syzygy degrees. Fel…

While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…

We give an application of the New Intersection Theorem and prove the following: let $R$ be a local complete intersection ring of codimension $c$ and let $M$ and $N$ be nonzero finitely generated $R$-modules. Assume $n$ is a nonnegative…

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…

A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed p-adic fields.…

We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.