Related papers: Divisorial contractions of algebraic varieties

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

This paper has been withdrawn by the author, due a critical mistake on page 3.

This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.

A foliation is of toric type when it has a combinatorial reduction of singularities. We show that every toric type foliation on (C3, 0), without saddle-nodes, has invariant surface. We extend the argument of Cano-Cerveau, done for the…

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

We exhaustively analyze the toric symmetries of CP^3 and its toric blowups. Our motivation is to study toric symmetry as a computational technique in Gromov-Witten theory and Donaldson-Thomas theory. We identify all nontrivial toric…

This paper has been withdrawn by the author. A much more revised version is available as arXiv:0909.4238.

This paper has been withdrawn due to an error in the proof of Theorem 5.3.

Every three-fold divisorial contraction to a non-Gorenstein point is a weighted blow-up.

We develop a ring-theoretic approach for blowing up many noncommutative projective surfaces. Let T be an elliptic algebra (meaning that, for some central element g of degree 1, T/gT is a twisted homogeneous coordinate ring of an elliptic…

We construct and study noncommutative deformations of toric varieties by combining techniques from toric geometry, isospectral deformations, and noncommutative geometry in braided monoidal categories. Our approach utilizes the same fan…

This paper has been withdrawn by the author due to an error in the proof of Theorem 1.

We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.

This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…

In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions. In particular, we describe to which components each such deformation maps, show how…

We study degenerations of cluster type varieties and pairs. Our first theorem proves that degenerations of toric pairs are finite quotients of toric pairs. In a similar vein, under some mild conditions, we prove that degenerations of…

It is shown that the conclusion [arXiv:1208.1166v2] made by Porsch and R\"oseler that their cutoff polaron theory transforms to Tulub theory is erroneous. The results of the work by Klimin and Devreese based on the results of Porsch and…

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

We prove that the $p^\infty$-torsion of the transcendental Brauer group of an abelian variety over a finitely generated field of characteristic $p>0$ is bounded. This answers a (variant of a) question asked by Skorobogatov and Zarhin for…

This paper has been withdrawn by the author due to a critical error in the proof of Theorem 5.4 on which the proof of the main theorem on the non-simplenss was based.