Related papers: Analytic Bertini theorem
We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.
We present a new proof of a Finslerian version of Beltrami's theorem (1865) which works also in dimension 2.
In this paper, we introduce a new connector which generalizes the connector found by the third author and Yamamoto. The new connector gives a direct proof of the double Ohno relation recently proved by the first author, the second author,…
After reviewing Bertini's life story, a fascinating drama, we make a critical examination of the old statements and proofs of Bertini's two fundamental theorems, the theorem on variable singular points and the theorem on reducible linear…
In this lecture we prove a converse to Cartan's Theorem B for real analytic sets, due to Fernando and Ghiloni [arXiv:2506.18347].
We prove Union-Closed sets conjecture.
We prove an analogue of the Centralizer Theorem in the context of Artin-Tits groups.
We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods.
We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.
We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.
Let $X$ be an irreducible projective variety and $f$ a morphism $X \rightarrow \mathbb{P}^n$. We give a new proof of the fact that the preimage of any linear variety of dimension $k\ge n+1-\dim f(X)$ is connected. We prove that the…
We show that Fueter's theorem holds for a more general class of quaternionic functions than those constructed by the Fueter's method.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
We prove that strongly F-regular and F-pure singularities satisfy Bertini-type theorems (including in the context of pairs) by building upon a framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and Spreafico). We…
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend…