Related papers: On arithmetic general theorems for polarized varie…

As a discrete counterpart to the classical John theorem on the approximation of (symmetric) $n$-dimensional convex bodies $K$ by ellipsoids, Tao and Vu introduced so called generalized arithmetic progressions $P(A,b)\subset Z^n$ in order to…

We prove a semiample generalization of Poonen's Bertini Theorem over a finite field that implies the existence of smooth sections for wide new classes of divisors. The probability of smoothness is computed as a product of local…

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the…

In this paper, we prove a general second main theorem for meromorphic mappings into a subvariety $V$ of $\mathbb P^N(\mathbb C)$ with an arbitrary family of moving hypersurfaces. Our second main theorem generalizes and improves all previous…

We give a proof of Pixton's generalized Faber-Zagier relations in the tautological Chow ring of $\overline M_{g,n}$. The strategy is very similar to the work of Pandharipande-Pixton-Zvonkine, who have given a proof of the same result in…

We prove a generalisation of Roth's theorem for arithmetic progressions to d-configurations, which are sets of the form {n_i+n_j+a}_{1 \leq i \leq j \leq d} where a, n_1,..., n_d are nonnegative integers, using Roth's original density…

In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…

In this addendum we generalize some results of our article "Generically split projective homogeneous varieties", Duke Math. J. 152 (2010), no. 1, 155-173. More precisely, we remove all restrictions on the characteristic of the base field…

This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory,…

We formulate and prove an analog of Poonen's finite-field Bertini theorem with Taylor conditions that holds in the Grothendieck ring of varieties. This gives a broad generalization of the work of Vakil-Wood, who treated the case of smooth…

Given a projective variety X defined over a finite field, the zeta function of divisors attempts to count all irreducible, codimension one subvarieties of X, each measured by their projective degree. When the dimension of X is greater than…

We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory. The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the…

The purpose of this note is to give a simple proof of the following theorem: Let $X$ be a normal projective variety over an algebraically closed field $k$, $\op{char} k = 0$ and let $D \subset X$ be a proper closed subvariety of $X$. Then…

We prove Vojta's abc conjecture for projective space ${\Bbb P}^n({\Bbb C})$, assuming that the entire curves in ${\Bbb P}^n({\Bbb C})$ are highly ramified over the coordinate hyperplanes. This extends the results of Guo Ji and the…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

Given a class of functions $F$ on a probability space $(\Omega,\mu)$, we study the structure of a typical coordinate projection of the class, defined by $\{(f(X_i))_{i=1}^N : f \in F\}$, where $X_1,...,X_N$ are independent, selected…

We develop a theory of Mackey functors on epiorbital categories which simultaneously generalizes the theory of genuine $G$-spectra for a finite group $G$ and the theory of $n$-excisive functors on the category of spectra. Using a new theory…

In this paper we study extension theorems associated with general varieties in two dimensional vector spaces over finite fields. Applying Bezout's theorem, we obtain the sufficient and necessary conditions on general curves where sharp…

The purpose of this paper has twofold. The first is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of…

We construct relative Gromov--Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a simple normal crossings pair $(X,D)$, we show that there…