Related papers: Divisorial contractions of algebraic varieties

This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic constructions, subjects touched on include…

The paper has been withdrawn due to an error in the main theorem.

We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans…

This paper has been withdrawn due to a crucial error in the proof of the main theorem

This paper has been withdrawn by the author due to a crucial error in the formulation.

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative projective surfaces (or, slightly more generally, of noetherian connected graded domains of Gelfand-Kirillov dimension 3). In a…

This paper was withdrawn (temporarily?) by the author since an error needs to be corrected.

In the previous version of the paper it was announced that ``sphere homeomorphic flexible polyhedra (with self intersections) do really exist in n-dimensional Euclidean, Lobachevskij and spherical spaces for each $n\geq 3$.'' Now the paper…

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

This is a pedagogical review on $\mathrm{T}\overline{\mathrm{T}}$ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts.…

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a unique turning point in…

Due to a significant error in the main result (pointed out by J. Wahl), the paper has been withdrawn by the authors. A corrected and expanded version is 'Rational blow-downs and smoothings of surface singularities' by A. Stipsicz, Z. Szabo…

This paper has been withdrawn by the author, due an error in computing the invariance of the so(4,1) and so(3,2) "inner product."

We give a simpler and more conceptual proof that a morphism from a 3-fold to a surface, over an algebraically closed field of characteristic 0, can be made into a toroidal morphism by sequences of blow ups of nonsingular subvarieties above…

We show that toric surface singularities deform to toric surface singularities - both in equal and mixed characteristic. As an application, we establish Riemenschneiders conjecture that isolated cyclic quotient singularities of any…

This paper has been withdrawn by the author due to an error in the proof of Theorem 6.

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime…