Related papers: Bounds on Fake Weighted Projective Space

Let $\Lambda$ be an artin algebra. We give an upper bound for the dimension of the bounded derived category of the category $\mod \Lambda$ of finitely generated right $\Lambda$-modules in terms of the projective and injective dimensions of…

We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…

We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^p-L^q$ spaces, with $1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are only assumed to…

Consider the weight $\lambda$ which is the sum of all simple roots of a simple Lie algebra. Using Kostant's weight multiplicity formula we describe and enumerate the contributing terms to the multiplicity of the zero weight in the…

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\,\mathbb{R}^n,w_1)\times\dots\times L^{p_m}(l^{q_m};\,\mathbb{R}^n,w_m)$ to…

We study global deformations of certain projective bundles over projective spaces. We show that any projective global deformation of a projective bundle over $\bP^1$ carries the structure of a projective bundle over some projective space.…

In this paper we provide some exact formulas for projective dimension and the regularity of powers of edge ideals of vertex-weighted rooted forests. These formulas are functions of the weight of the vertices and the number of edges. We also…

We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…

Let $n \geq 2$ be an integer such that an equiangular set of vectors $w_1, \ldots, w_d$ of the maximal possible cardinality (in relation to the the general Gerzon upper bound) exists in $\mathbb{K}^n$, where $\mathbb{K}=\mathbb{R}$ or…

The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the…

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to those of the usual projective plane. They come in complex conjugate pairs and have been classified as quotients of the two-dimensional ball by…

The topological complexity ${\sf TC}(X)$ is a homotopy invariant of a topological space $X$, motivated by robotics, and providing a measure of the navigational complexity of $X$. The topological complexity of a connected sum of real…

Let $F \in \mathbf{Z}[\boldsymbol{x}]$ be a diagonal, non-singular quadratic form in $4$ variables. Let $\lambda(n)$ be the normalised Fourier coefficients of a holomorphic Hecke form of full level. We give an upper bound for the problem of…

We present a general classification algorithm for reflexive simplices, which allows us to determine all reflexive simplices in dimensions five and six. In terms of algebraic geometry this means that we classify the Gorenstein fake weighted…

Let X be a Fano manifold of pseudoindex i_X whose Picard number is at least two and let R be an extremal ray of X with exceptional locus Exc(R). We prove an inequality which bounds the length of R in terms of i_X and of the dimension of…

In this paper, we prove an upper bound on the second non-zero Laplacian eigenvalue on $n$-dimensional real projective space. The sharp result for 2-dimensions was shown by Nadirashvili and Penskoi and later by Karpukhin when the metric…

Let $X\subset \mathbb P^d$ be a $m$-dimensional variety in $d$-dimensional projective space. Let $k$ be a positive integer such that $\binom{m+k}k \le d$. Consider the following interpolation problem: does there exist a variety $Y\subset…

We prove that if $f$ is a reduced homogenous polynomial of degree $d$, then its $F$-pure threshold at the unique homogeneous maximal ideal is at least $\frac{1}{d-1}$. We show, furthermore, that its $F$-pure threshold equals $\frac{1}{d-1}$…

We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang's conjecture on rational points of hyperbolic varieties, we use this to prove that a projective variety with only finitely many…

A fake projective plane is a smooth complex surface which is not the complex projective plane but has the same Betti numbers as the complex projective plane. The first example of such a surface was constructed by David Mumford in 1979 using…