Related papers: Finding a field in a Zariski-like structure

As a consequence of the Riemann-Roch theorem, a closed Riemann surface $S$ can be described by a non-singular complex projective algebraic curve $C$. A field of definition for $S$ is any subfield $D$ of $\mathbb{C}$ so that we may choose…

Let K be a field not of characteristic 2 such that every finite separable extension of K is cyclic. Let A be an abelian variety over K. If K is infinite, then A(K) is Zariski-dense in A. If K is not locally finite, the rank of A over K is…

We show that the existence of a birational weak Zariski decomposition for a pseudo-effective generalized polarized lc pair is equivalent to the existence of a generalized polarized log terminal model.

The aim of this work is to firstly demonstrate the efficacy of the recently proposed Orlicz space formalism for Quantum theory \cite{ML}, and secondly to show how noncommutative differential structures may naturally be incorporated into…

We attach a Dixmier algebra B to the closure of any nilpotent orbit of G where G is GL(n,C), O(n,C) or Sp(2n,C). This algebra B is a noncommutative analog of the coordinate ring R of the orbit closure, in the sense that B has a G-invariant…

Let $M$ be a compact hyperkaehler manifold. The hyperkaehler structure equips $M$ with a set $R$ of complex structures parametrized by $CP^1$, called "the set of induced complex structures". It was known previously that induced complex…

We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory $T$ is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model $M$ of $T$ has an expansion…

We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure $M$. We prove that if $T$ is a complete $L$-theory, then $T$ is mutually algebraic if and only if there is some model $M$ of $T$ for…

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…

Given a Morse function f on a closed manifold M with distinct critical values, and given a field F, there is a canonical complex, called the Morse-Barannikov complex, which is equivalent to any Morse complex associated with f and whose form…

We study the Zariski closure of the monodromy group $\mathbf{Mon}$ of Lauricella's hypergeometric function $F_C$. If the identity component $\mathbf{Mon}^0$ acts irreducibly, then $\overline{\mathbf{Mon}} \cap \mathbf{SL}_{2^n}(\mathbb{C})$…

The main properties of indefinite Kac-Moody and Borcherds algebras, considered in a unified way as Lorentzian algebras, are reviewed. The connection with the conformal field theory of the vertex operator construction is discussed. By the…

The structure of classical non-linear $\cw$ algebras closing on rational functions is analyzed both for the ordinary and the supersymmetric case. Such algebras appear as a result of a coset construction. Their relevance to physical…

Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear…

Tensor triangular geometry as introduced by Balmer is a powerful idea which can be used to extract the ambient geometry from a given tensor triangulated category. In this paper we provide a general setting for a compactly generated tensor…

A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have…

We develop a general theory of Cartesian and non-Cartesian polynomials on products of complex spaces $\mathbb{C}^{n_1} \times \cdots \times \mathbb{C}^{n_k}$. We prove that, for any fixed degree $d \ge 2$, a (Zariski) generic polynomial is…

We prove the Zariski dense orbit conjecture in positive characteristic for endomorphisms of $\mathbb{G}_a^N$ defined over $\overline{\mathbb{F}_p}$.

Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the first mod m Suslin homology and the first…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.