Related papers: Combinatorial classification of $(\pm 1)$-skew pro…

In this essay we study various notions of projective space (and other schemes) over $\mathbb{F}_{1^\ell}$, with $\mathbb{F}_1$ denoting the field with one element. Our leading motivation is the "Hiden Points Principle," which shows a huge…

It is shown that a trace invariant projection map, i.e. a positive unital idempotent map, of a finite dimensional C*-algebra into itself is non-decomposable if and only if it is atomic, or equivalently not the sum of a 2-positive and a…

An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a…

A subspace of an algebra with involution is called a Lie skew-ideal if it is closed under Lie products with skew-symmetric elements. Lie skew-ideals are classified in central simple algebras with involution (there are eight of them for…

This is a little investigation into the classification of complexes of direct sums of line bundles on projective spaces. We consider complexes on projective k-space Pk : O_Pk(-1)^a --> O_Pk^b --> O_Pk(1)^c, with the first map injective and…

We represent stationary descendant Gromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of large degree behaviour of stationary descendant…

Let $V$ and $V'$ be vector spaces over division rings (possible infinite-dimensional) and let ${\mathcal P}(V)$ and ${\mathcal P}(V')$ be the associated projective spaces. We say that $f:{\mathcal P}(V)\to {\mathcal P}(V')$ is a PGL-{\it…

The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…

We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of non-linear isotopies of cubic norm structures, and one in terms of hermitian cubic norm structures.…

In this paper, we study the divisor theory of the Simpson moduli space of semistable sheaves of dimension 1 on the projective plane. We prove that these spaces are all Mori dream spaces, and calculate their nef cones. We also study the…

Given a smooth complex variety $X$, an algebraically skew embedding of $X$ is an embedding of $X$ into a complex projective space $\mathbb{P}^N$ such that for any two points $x,y\in X$, their embedded tangent spaces in $\mathbb{P}^N$ do not…

In this article we provide a classification of the projective transformations in $PSL(n+1,\Bbb{C})$ considered as automorphisms of the complex projective space $\Bbb{P}^n$. Our classification is an interplay between algebra and dynamics,…

We study skew-symmetrizable cluster algebras $\mathcal{A}$ associated with unpunctured surfaces $\tilde{\mathbf{S}}$ endowed with an orientation-preserving involution $\sigma$. We give a geometric realization of such cluster algebras by…

We compute the equivariant homology and cohomology of projective spaces with integer coefficients. More precisely, in the case of cyclic groups, we show that the cellular filtration of the projective space $P(k\rho )$, of lines inside…

It is shown that the projection image of an oriented spatial arc to any oriented plane is approximated by a unique arc diagram (up to isomorphic arc diagrams) determined from the spatial arc and the projection. In a separated paper, the…

We pose and solve the equivalence problem for subspaces of ${\mathcal P}_n$, the $(n+1)$ dimensional vector space of univariate polynomials of degree $\leq n$. The group of interest is ${\rm SL}_2$ acting by projective transformations on…

A Littlewood polynomial is a single-variable polynomial all of whose coefficients lie in $\{ \pm 1\}$. We establish the leading term asymptotics of the number of reciprocal or skew-reciprocal Littlewood polynomials with square discriminant.…

We survey and expand on the work of Segal, Milgram and the author on the topology of spaces of maps of positive genus curves into $n$-th complex projective space, $n\geq 1$ (in both the holomorphic and continuous categories). Both based and…

Two quasi-projective varieties are called piecewise isomorphic if they can be stratified into pairwise isomorphic strata. We show that the m-th symmetric power $S^m(C^n)$ of the complex affine space $C^n$ is piecewise isomorphic to $C^{mn}$…

We consider the Poisson algebra S(M) of smooth functions on T^*M which are fiberwise polynomial. In the case where M is locally projectively (resp. conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp.…