Related papers: Birational geometry and localisation of categories

This paper has been withdrawn by the author due a few mistakes in the paper.

The main result can be given a short and elementary proof which has been incorporated into Lemma 3.2 of arXiv:1206.5775

In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the…

Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing of the last section.

This paper has been withdrawn, because I have merged it with paper I of the series, math.AG/0312190. The main results of this paper now appear in sections 7-9 of the revised version of math.AG/0312190, with shortened and improved proofs.

The statement of Lemma 3.1 in the published paper is not correct. Lemma 3.1 is needed for the proof of Theorem 3.2. Theorem 3.2 as originally stated is true but its "proof" is not correct. Here we change the statements and proofs of Lemma…

We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagrams represent the same morphism if and only if they can be…

This article has been withdrawn due to an error in a proof of the main result.

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

A behavior of one class of mappings with finite distortion at a neighborhood of the origin is investigated. There is proved a lower estimate of distortion of a distance under mappings mentioned above.

New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for…

In the proof of Lemma 2.6 (2) the iteration of the map {\tau} was not performed properly and in fact the lemma is wrong; a counterexample is given by f = \bar{x}_1and k = 2. This error does not, however, affect the geometric…

We establish a bi-equivalence between the bi-category of topoi with enough points and a localisation of a bi-subcategory of topological groupoids

We give a corrected version of Corollary 3.33 in: H. Flenner, S. Kaliman, and M. Zaidenberg, Birational transformations of weighted graphs. Affine algebraic geometry. Osaka Univ. Press, 2007, 107-147.

This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation functors to an appropriate bicategory of artinian DG…

In this short note, we give a localized version of the basic triangle theorem, first published in 2011 (see [4]) in order to prove the independence of hyperlogarithms over various function fields. This version provides direct access to…

We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera. Version 2: small changes in first half. Improved version of the second half is now a separate…

We prove that the 2-category of action Lie groupoids localised in the following three different ways yield equivalent bicategories: localising at equivariant weak equivalences \`a la Pronk, localising using surjective submersive equivariant…

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.

We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.