Related papers: Questions on self maps of algebraic varieties
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
We study varieties defined over nonstandard fields using techniques of nonstandard mathematics.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
This is the expanded version of my talk at the workshop "Groups of Automorphisms in Birational and Affine Geometry", October 29--November 3, 2012, Levico Terme, Italy. The first section is focused on Jordan groups in abstract setting, the…
This is an expository paper in which we define projective GIT quotients and introduce toric varieties from this perspective. It is intended primarily for readers who are learning either invariant theory or toric geometry for the first time.
We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe when two relative symmetric powers of projective bundles…
This paper deals with holomorphic self-maps of the complex projective plane and the algebraic relations among the eigenvalues of the derivatives at the fixed points. These eigenvalues are constrained by certain index theorems such as the…
Geometric Invariant Theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev-Hu and Thaddeus, it is known that two…
A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
We describe the automorphism groups of elliptic Poisson algebras on polynomial algebras in three variables and give an explicit set of generators and defining relations for this group.
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…
We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.
We survey on algebraically elliptic varieties in the sense of Gromov.
The paper surveys various Waring type problems in groups, Lie algebras, and associative algebras.
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.