Related papers: On Toric Orbits in the Affine Sieve

We study the periodic orbits problem on energy levels of Tonelli Lagrangian systems over configuration spaces of arbitrary dimension. We show that, when the fundamental group is finite and the Lagrangian has no stationary orbit at the…

In the previous work, we study the moment polytope of the closure of the complex subtorus orbit in a symplectic toric manifold associated to an affine subspace when the closure is a smooth complex submanifold. In this paper, we clarify the…

We prove the Zariski dense orbit conjecture in positive characteristic for regular self-maps of split semiabelian varieties.

A couple of complex projective plane curves are said to make a Zariski pair if they have the same degree and the same type of singularities, but their embeddings in the projective plane are topologically different. In this paper, we present…

We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…

Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…

We compare two formulas for the class of a generic torus orbit closure on the Grassmannian, due to Klyachko and Berget-Fink. The naturally emerging combinatorial objects are semi-standard fillings we call 1-strip-less tableaux.

This article is the first in a series of two in which we study the vanishing cycles of curves in toric surfaces. We give a list of possible obstructions to contract vanishing cycles within a given complete linear system. Using tropical…

Consider an algebraic torus of small dimension acting on an open subset of a complex vector space, or more generally on a quasiaffine variety such that a separated orbit space exists. We discuss under which conditions this orbit space is…

Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…

The paper is devoted to a detailed self-contained exposition of a part of the theory of affine planes leading to a construction of affine (or, equivalently, projective) planes not satisfying the Desarques axiom. It is intended to complement…

Let $X/K$ be a smooth projective variety defined over a number field, and let $f:X\to{X}$ be a morphism defined over $K$. We formulate a number of statements of varying strengths asserting, roughly, that if there is at least one point…

Properties of inertial modes of Jupiter are investigated for an n=1 polytropic description of the planet interior. We use the anelastic approximation to overcome the usual handicap of a severe spherical harmonics truncation. A powerful…

Given an affine variety $X$, a morphism $\phi:X\to X$, a point $\alpha\in X$, and a Zariski closed subset $V$ of $X$, we show that the forward $\phi$-orbit of $\alpha$ meets $V$ in at most finitely many infinite arithmetic progressions, and…

We prove a product decomposition of the Zariski closure of the jet lifts of a holomorphic map f from C into a semi-abelian variety A, provided that f is of finite order. On the other hand, by giving an example of such a map f into a three…

This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…

We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can…

Let T be a maximal torus in a classical linear group G. In this paper we find all simple rational G-modules V such that for each vector v in V the closure of its T-orbit is a normal affine variety. For every other G-module we present a…

On a smooth algebraic variety over $\mathbb{C}$, we build the tempered subanalytic and Stein tempered subanalytic sites. We construct the sheaf of holomorphic functions tempered at infinity over these sites and study their relations with…

Given an action of an algebraic torus on a normal affine variety, we describe all open subsets admitting a complete orbit space.