相关论文: Stability of algebraic varieties and Kahler geomet…

This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.

Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.

We survey some recent developments in the study of canonical K\"{a}hler metrics on algebraic varieties and their relation with stability in algebraic geometry.

Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk\"ahler geometry and classical algebraic geometry.

This is a survey of results on the Hilbert property of algebraic varieties, and variants of it.

This expository article is based on the author's talk at the Kinosaki Algebraic Geometry Symposium 2025. We discuss some recent progress surrounding stable degeneration in algebraic K-stability theory.

We survey some recent results and constructions of almost-K\"ahler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.

We review recent developments in the theory of compact hyper-K\"ahler varieties, from the viewpoint of Lagrangian fibrations, moduli spaces of stable sheaves, and derived categories. These notes originated from the lecture by the second…

Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…

This survey article is a much extended version of a lecture given at a Clay Institute workshop in October 2006. It describes all known results on the existence of stable coherent systems on algebraic curves.

This is a survey paper on Alegbraic Geometry over Lie Algebras

We show how to formulate some recent results from homological stability of algebras in Graham and Lehrer's language of cellular algebras. The aim is to begin to connect the new results from topology to well-established representation…

We give a survey of the recent progress on the study of K-stability of Fano varieties by an algebro-geometric approach.

This survey article is an accompaniment to the 2025 Summer Research Institute in Algebraic Geometry Bootcamp on K-stability and K-moduli. It is aimed at graduate students and intended to provide the necessary background to begin research on…

This is a survey paper that also contains some new results. It will appear in the proceedings of the AMS summer research institute on Algebraic Geometry at Santa Cruz.

We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.

We give an algebro-geometric or non-archimedean framework to study bubbling phenomena of Kahler metrics with Euclidean volume growth, after [DS17, Sun23, dBS23]. In particular, for any degenerating family to log terminal singularity, we…

This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…

These lecture notes are written for a PhD mini-course I gave at the CIRM in Luminy in 2019. Their intended purpose was to present, in the context of smooth toric varieties, a relatively self-contained and elementary introduction to the…

This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…