Related papers: D\'eformations des courbes rationnelles

This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.

In this short note, we explain how the main results in "$\tau$-tilting theory" by Adachi-Iyama-Reiten follow from the results in Section 5 of "General presentations of algebras" by Derksen-Fei.

This note simplifies the proof of a recent result on the oscillation of the prime product in Martens Theorem, and provides a quantitative expression for the error term. In addition, the corresponding oscillation results for the finite sums…

We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.

We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, and we provide numerical evidence…

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

Several new applications of Katona's circle are given.

Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of math.QA/0504420 contains an error. In this note I give a correct proof of this lemma which was suggested to me by Dmitry Tamarkin. The correction does not change the results…

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

In this note we give geometric formulations and proofs of three results of S. Morita. These results relate certain two dimensional cohomology classes of various moduli spaces of curves. We also give a geometric interpretation of a fourth…

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

Matsumoto proved in arXiv:1012.0981 that the prime end rotation numbers associated to an invariant annular continuum are contained in its rotation set. An alternative proof of this fact using only simple planar topology is presented.

We present a critical review of the relativistic rotation transformation of Trocheris and Takeno. A new transformation is proposed which is free from the drawbacks of the former. Some applications are presented.

This paper has been withdrawn by the author due to a crucial error in equation (51).

Dumitru Popa found asymptotic expansions for certain nonlinear recurrences, but left open the numerical evaluation of associated constants. We address this issue. A change of variables involving reciprocals and the algorithm of Mavecha &…

Work in progress concerning alternative formalizations of arithmetic.

Recently Baranyai described a necessary combinatorial characterisation of graph rigidity for dimension 3. In this short note we provide a counter-example to the converse of the condition. Additionally, we provide an alternative proof to the…

This note provides a generalisation of a recent result by J\"arvenp\"a\"a, J\"arvenp\"a\"a, Koivusalo, Li, and Suomala, (to appear), on the dimension of limsup-sets of random coverings of tori. The result in this note is stronger in the…

An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…

We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also…