Related papers: A going-up theorem
Based on various strategies and a new general doubling operator, we obtain several simple proofs of the celebrated Sharkovsky's cycle coexistence theorem. A simple non-directed graph proof which is especially suitable for a calculus course…
An technically interesting proof of a known theorem.
We show how to obtain the Zariski invariant of a plane branch employing the contact order or the intersection multiplicity with elements in a particular family of curves and we present some consequences of this result.
In algebraic geometry specialisations and valuations play and important role. In this paper we start investigating analogous structures for Zariski structures. Specifically, we look into the existence and uniqueness properties of extensions…
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…
We prove the Zariski dense orbit conjecture in positive characteristic for regular self-maps of split semiabelian varieties.
In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.
We generalize Rado's extension theorem to complex spaces.
In this note we give a quick and simple proof of the existence (and uniqueness) of Zariski decompositions on surfaces. While Zariski's original proof employs a rather sophisticated procedure to construct the negative part of the…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation…
We prove a generic Torelli theorem for Jacobian elliptic surfaces, provided that the geometric genus is large compared to the irregularity. The result is effective to the extent that defining equations for the base curve are recovered from…
We construct a Zariski decomposition for cycle classes of arbitrary codimension. This decomposition is an analogue of well-known constructions for divisors. Examples illustrate how Zariski decompositions of cycle classes reflect the…
We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.
We prove a uniformization theorem in complex algebraic geometry.
In this paper, we study a point-hyper plane incidence theorem in matrix rings, which generalizes all previous works in literature of this direction.
The so-called type problem or forcing problem is considered as a way to generalize Sharkovskii's theorem. In this paper, by focusing on certain types of orbits, we obtain a solution of the type problem, which gives a refinement of…
We establish two direct extensions to the Butterfly Theorem on the cyclic quadrilateral along with the proofs using the projective method and analytic geometry of the Cartesian coordinate system.
Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Brou\'e-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for…
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof.…