Related papers: A strange example concerning Property N_p

Let $X \subset \P^r$ be a nondegenerate projective variety and let $\nu_{\ell} : \P^r \to \P^N$ be the $\ell$-th Veronese embedding. In this paper we study the higher normality, defining equations and syzygies among them for the projective…

Let $p$ be an odd prime and let $k$ be a field of characteristic $p$. We provide a practical algebraic description of the representation ring of $k\mathrm{SL}_2(\mathbb{F}_p)$ modulo projectives. We then investigate a family of modular…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

Let $M$ be a compact manifold of dimension at least 2. If $M$ admits a minimal homeomorphism then $M$ admits a minimal noninvertible map.

We show that if C is a linearly normal smooth curve embedded by a line bundle of degree at least 2g+3+p then the secant variety to the curve satisfies N_{3,p}.

For a submodule $N$ of an $R$-module $M$, a unique product of prime ideals in $R$ is assigned, which is called the generalized prime ideal factorization of $N$ in $M$, and denoted as ${\mathcal{P}}_M(N)$. But for a product of prime ideals…

Let L be a positive line bundle on a projective complex manifold. We study the asymptotic behavior of Bergman kernels associated with the tensor powers L^p of L as p tends to infinity. The emphasis is the dependence of the uniform estimates…

Let $1<p,\,q<\infty$. It is shown for complex scalars that there are no nontrivial $M$-ideals in $L(L_p[0,1])$ if $p\neq 2$, and $K(\ell_p(\ell_q^n)$ is the only nontrivial $M$-ideal in $L(\ell_p(\ell_q^n)$. This proves a conjecture of…

We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is…

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

In 2014, Benjamin Nachman showed that when $p\equiv$1 mod 8, the 2-dimensional projective linear group over the field of $p$ elements fails the replacement property if the maximal length $m$ of an irredundant generating sequence for the…

Starting from an integral projective variety $Y$ equipped with a very ample, non-special and not-secant defective line bundle $\mathcal{L}$, the paper establishes, under certain conditions, the regularity of $(Y \times \mathbb…

This paper deals with the class of existentially closed models of fields with a distinguished submodule (over a fixed subring). In the positive characteristic case, this class is elementary and was investigated by the first-named author.…

Let a Poisson structure on a manifold M be given. If it vanishes at a point m, the evaluation at m defines a one dimensional representation of the Poisson algebra of functions on M. We show that this representation can, in general, not be…

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…

We prove an elementary but somewhat unexpected result about projective embeddings of smooth varieties X whose cotangent bundles are numerically effective. Specifically, we show that the degree of X in any projective embedding must grow…

Let X be a smooth irreducible complex projective curve of genus g > 1. In this paper, we give necessary and sufficient conditions for an unstable bundle of HN-lenght 2 to have a particular algebra of endomorphisms. Then, fixing the…

We construct the first examples of manifolds, the simplest one being the product of S^3, S^4, and R^5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls.

Let $p>2$ be a prime. We give examples of smooth absolutely irreducible representations of $\mathrm{GL}_2(\mathbb{Q}_{p^3})$ over $\mathbb{F}_{p^3}$ which are not admissible.

We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. J. Wahl characterized projective…