相关论文: On Boris Moishezon's multiple planes

This is the (revised) printed version of the talk no 1056 (june 2012) of the Bourbaki seminar, which will be published in an Ast\'erisque volume. This is a report on a paper by Hrushovski and Loeser (/arxiv:1009.0252). In this paper they…

This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.

These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…

A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by…

These are largely expanded notes from lectures on Higgs moduli and abelianisation given in Angers, France (2014) and Guaruja, Brazil (2015). Dedicated to Ugo Bruzzo on his 60-th birthday. Version 2: minor corrections.

Toric varieties are perhaps the most accessible class of algebraic varieties. They often arise as varieties parameterized by monomials, and their structure may be completely understood through objects from geometric combinatorics. While…

This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…

This article will appear in the proceedings of the AMS Summer Institute in Algebraic Geometry at Santa Cruz, July 1995. The topic is toric ideals, by which I mean the defining ideals of subvarieties of affine or projective space which are…

This is a resume of the talk delivered at the Symposium on Hodge theory, Degeneration and Complex surfaces, Tagajo, Miyagi, March 2004.

This is the text of the Hermann Weyl Prize lecture given by the author at the XXIV Colloquium on Group Theoretical Methods in Physics, Paris, July 2002 (to appear in the Proceedings of the Colloquium).

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

Lectures deliverd at the NATO Advanced Study Institute on QCD Perspectives on Hot and Dense Matter, Cargese, Aug. 6 - 18, 2001. Dedicated to the memory of Dominique Vautherin.

This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and…

This article is based on a series of lectures on toric varieties given at RIMS, Kyoto. We start by introducing toric varieties, their basic properties and later pass to more advanced topics relating mostly to combinatorics.

These are lecture notes for the course "Poisson geometry and deformation quantization" given by the author during the fall semester 2020 at the University of Zurich. The first chapter is an introduction to differential geometry, where we…

This paper is a natural continuation of paper "On rectifiable spaces and its algebraical equivalents, topological algebraic systems and Mal'cev algebras" published in arxiv:1309.4572. Thus we justify the need to present the entire material…

The goal of these talks was to explain how cohomology and other tools of algebraic topology are seen through the lens of n-category theory. Special topics include nonabelian cohomology, Postnikov towers, the theory of "n-stuff", and…

We study multihomogeneous spaces corresponding to ${\mathbb Z}^n$-graded algebras over an algebraically closed field of characteristic 0 and their relation with the description of $T$-varieties.

These are the notes of a lecture held by Michael Hopkins in march 2007, at the Talbot workshop.

For phase-space manifolds which are compact Kaehler manifolds relations between the Berezin-Toeplitz quantization and the quantization with the help of Berezin's coherent states and symbols are studied. First the results on the…