Related papers: Birational geometry and localisation of categories
We describe a bicategory $(\mathcal{R}ed\,\mathcal{O}rb)$ of reduced orbifolds in the framework of classical differential geometry (i.e. without any explicit reference to notions of Lie groupoids or differentiable stacks, but only using…
We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.
I withdraw the previous version of the paper since it contains conceptual and mathematical mistakes. I will soon replace it with a radically revised version.
The purpose of this note is make Theorem 13 in the article "On Biautomaticity of Non-Homogenous Small-Cancellation Groups" more accessible. Restatements of the theorem already appeared in few of the authors' succeeding works but with no…
In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective…
We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category…
3D object detection and pose estimation from a single image are two inherently ambiguous problems. Oftentimes, objects appear similar from different viewpoints due to shape symmetries, occlusion and repetitive textures. This ambiguity in…
Given a functor $T:C \to D$ carrying a class of morphisms $S\subset C$ into a class $S'\subset D$, we give sufficient conditions in order that $T$ induces an equivalence on the localised categories. These conditions are in the spirit of…
In this short note, we complete the description of low-degree characteristic classes of oriented 3-plane bundles over a 6-complex. Our goal is to point out and correct an error in L. M. Woodward's 1982 paper "The classification of principal…
In this short expository note, we discuss, with plenty of examples, the bestiary of fibrations in quasicategory theory. We underscore the simplicity and clarity of the constructions these fibrations make available to end-users of higher…
The result in theorem 2.1 has been strengthened (see theorem 2.3) and the remarks in the introduction and the text adapted to this new result. Also some misprints in the previous version have been corrected.
In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under…
Estimate (3.39) which appears in the proof of Proposition 3.4 in [Ann. Probab. 27 (1999) 1414--1467, doi:10.1214/aop/1022677454] is wrong. We present below a corrected proof which introduces an extra factor 2 in equations (3.34) and (3.35).…
We introduce new obstructions to rationality for geometrically rational threefolds arising from the geometry of curves and their cycle maps.
Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of…
We correct an error in the second part of Theorem 3 of our original paper (arXiv:1512.07161).
We correct an error in the paper referred to in the title. Part of the argument is organized as a general method for establishing when (derived) functors factor through a fixed Serre subcategory, which may be of some more general interest.
This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas
In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.
We give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups.