相关论文: Correction to "Fibers of tropicalization"

This paper has been withdrawn by the authors due to an error in the main theorem.

The purpose of this paper is to establish analogues of the classical Lefschetz Section Theorem for smooth tropical varieties. More precisely, we prove tropical analogues of the section theorems of Lefschetz, Andreotti-Frankel,…

Let $f(a,b,c,d)=\sqrt{a^2+b^2}+\sqrt{c^2+d^2}-\sqrt{(a+c)^2+(b+d)^2}$, let $(a,b,c,d)$ stand for $a,b,c,d\in\mathbb Z_{\geq 0}$ such that $ad-bc=1$. Define \begin{equation} \label{eq_main} F(s) = \sum_{(a,b,c,d)} f(a,b,c,d)^s.…

Building on our earlier work on toric residues and reduction, we give a proof for the mixed toric residue conejecture of Batyrev and Materov. We simplify and streamline our technique of tropical degenerations, which allows one to…

The tropical arithmetic operations on $\mathbb{R}$ are defined by $a\oplus b=\min\{a,b\}$ and $a\otimes b=a+b$. Let $A$ be a tropical matrix and $k$ a positive integer, the problem of Tropical Matrix Factorization (TMF) asks whether there…

The errors in the arguments, numerical results, and conclusions in the paper "Test of a modified BCS theory performance in the picket fence model" [Nucl. Phys. A 822 (2009) 1] by V.Yu. Ponomarev and A.I. Vdovin are pointed out. Its…

This version corrects a wrong proof of Proposition 6.3.2 and simplifies the exposition in Section 6.

We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on $[-\pi,\pi]$ having some singularities at the origin. Even though a sharp error order of the above…

This note corrects some omissions in section 2 of the paper "Lipschitz connectivity and filling invariants in solvable groups and buildings."

We prove a fundamental theorem for tropical partial differential equations, analogous to the fundamental theorem of tropical geometry in this context. We extend results from Aroca et al., Falkensteiner et al. and from Fink and Toghani for…

This paper has been withdrawn by the author, due to a crucial error in page 5.

This note is an (exact) copy of the report of Jaak Peetre, "Generalizing Ovchinnikov's Theorem". Published as Technical Report, Lund (1981). Some more recent general references have been added, some references updated though (in italics)…

This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem…

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

We disprove a conjecture of Foschi, regarding extremizers for the Strichartz inequality with data in the Sobolev space $\dot{H}^{1/2}\times\dot{H}^{-1/2}(\mathbb R^d)$, for even $d\ge 2$. On the other hand, we provide evidence to support…

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

We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…

We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums…

This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).

We introduce adic tropicalizations for subschemes of toric varieties as limits of Gubler models associated to polyhedral covers of the ordinary tropicalization. Our main result shows that Huber's adic analytification of a subscheme of a…