Related papers: Note on characterizations of projective spaces

The complex projective space $\mathbb{P}(\mathbb{C}^n)$ can be interpreted as the space of all quantum pure states of size $n$. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical…

We classify elliptic K3 surfaces in characteristic $p$ with $p^n$-torsion sections. For $p^n\geq3$ we verify conjectures of Artin and Shioda, compute the heights of their formal Brauer groups, as well as Artin invariants and Mordell--Weil…

Let $X\subseteq \mathbb{P}^N$ be a non-degenerate normal projective variety of codimension $e$ and degree $d$ with isolated $\mathbb{Q}$-Gorenstein singularities. We prove that the Castelnuovo-Mumford regularity…

We compute the Hilbert series of the space of $n=3$ variable quasi-invariant polynomials in characteristic $2$ and $3$, capturing the dimension of the homogeneous components of the space, and explicitly describe the generators in the…

In this paper we study the projective normality of certain Artin-Schreier curves $Y_f$ defined over a field $\F$ of characteristic $p$ by the equations $y^q+y=f(x)$, $q$ being a power of $p$ and $f\in \F[x]$ being a polynomial in $x$ of…

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…

Let k=F_q be a finite field of even characteristic. We obtain in this paper a complete classification, up to k-isomorphism, of non singular quartic plane curves defined over k. We find explicit rational normal models and we give closed…

We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and…

Let $X$ be a closed subscheme of codimension $e$ in a projective space. One says that $X$ satisfies property ${\bf N}_{d,p}$, if the $i$-th syzygies of the homogeneous coordinate ring are generated by elements of degree $<d+i$ for $0\le…

We prove a restricted projection theorem for Borel subsets of $\mathbb{Q}_p^n$ in the regime $p>n$. This generalizes results of Gan-Guo-Wang in the real setting. Our result is effective in the sense that explicit constants are obtained for…

We study the computational complexity of sequences of projective varieties. We define analogues of the complexity classes P and NP for these and prove the NP-completeness of a sequence called the universal circuit resultant. This is the…

We characterize operators $T=PQ$ ($P,Q$ orthogonal projections in a Hilbert space $H$) which have a singular value decomposition. A spatial characterizations is given: this condition occurs if and only if there exist orthonormal bases…

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…

The main aim of the paper is to provide analogues of Simpson's correspondence on singular projective varieties defined over an algebraically closed field of characteristic $p>0$. There are two main cases. In the first case, we consider…

We construct parabolic analogues of (global) eigenvarieties, of patched eigenvarieties and of (local) trianguline varieties, that we call respectively Bernstein eigenvarieties, patched Bernstein eigenvarieties, and Bernstein paraboline…

We study homotopy categories of model categories arising from a cotorsion triple, and the equivalences between corresponding stable categories. We characterize homological dimensions with respect to a cotorsion triple. Then, we lift…

We extend to characteristic $2$ and $3$ the classification of projective homogeneous varieties of Picard group isomorphic to $\mathbf{Z}$, corresponding to parabolic subgroup schemes with maximal reduced subgroup. The latter are all…

We describe the set of characteristic polynomials of abelian varieties of dimension 3 over finite fields.

We study universal polynomials of characteristic classes associated to the $\mathcal{A}$-classification (i.e. up to right-left equivalence) of holomorphic map-germs $(\mathbb{C}^2,0) \to (\mathbb{C}^n, 0)$ $(n=2,3)$. That enables us to…

We present a complete polarization characterization of any quantum state of two orthogonal polarization modes, and give a systematic measurement procedure to collect the necessary data. Full characterization requires measurements of the…