2 edition of Deformations of algebraic varieties with Gm action found in the catalog.
Deformations of algebraic varieties with Gm action
Henry C. Pinkham
Bibliography: p. 127-131.
|Statement||Henry C. Pinkham.|
|Series||Aste risque -- 20.|
|The Physical Object|
|Pagination||131 p. :|
|Number of Pages||131|
Book Jan Séminaire sur les singularités des surfaces / Centre de Mathématiques de l'Ecole Polytechnique, Palaiseau / edité par M. Demazure, H. Pinkham et B. Teissier. THE TOPOLOGY OF COMPLEX PROJECTIVE VARIETIES AFl-ER S. LEFSCHETZ 17 precise and at the same time easier to understand it is very convenient to modify (blow up) X along X’ to get a new variety Y with a map f: Y + G such that the fibres f .
Review of the birational geometry of curves and surfaces The minimal model program for 3-folds Towards the minimal model program in higher dimensions The strategy The conjectures of the MMP Mild singularities ∗ +∆ ∗ +∆). Christopher Hacon The File Size: KB. Algebraic Varieties, An Introduction Introduction An affine variety is an algebraic set with some rather nice properties. But before we dive into the math, let's have some words about words. Let K be a field and let C be its algebraic closure. A variety is an algebraic set, and an algebraic set is a region R in C n, such that a set of.
Algebraic Transformation Groups and Algebraic Varieties: Proceedings of the conference Interesting Algebraic Varieties Arising in Algebraic Transformation Group Theory held at the Erwin Schrödinger Institute, Vienna, October 22–26, Ciro Ciliberto, Vincenzo Di Gennaro (auth.), Vladimir L. Popov (eds.). Complex Algebraic Geometry MSRI Publications Vol Fundamental Groups of Smooth Projective Varieties DONU ARAPURA To the memory of Boris Moishezon Abstra ct. This article is a brief survey of work related to the structure of topological fundamental groups of complex smooth projective varieties.
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Additional Physical Format: Online version: Pinkham, H. (Henry). Deformations of algebraic varieties with Gm action. Paris: Société mathématique de France, Buy Deformations of Algebraic Schemes (Grundlehren der mathematischen Wissenschaften) on FREE SHIPPING on qualified ordersCited by: It includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, Hilbert schemes of points, local Picard functors, etc.
Many examples are provided. Most of. I found this book quite opaque in general, and not a good place to learn algebraic geometry as a subject, although the discussion of cohomology was relatively good. Kempf assumes familiarity with classical algebraic geometry and defines an algebraic variety as something obtained by glueing together (finitely many) classical varieties/5(3).
In one sense, deformation theory is as old as algebraic geometry itself: this is because all algebro-geometric objects can be “deformed” by suitably varying the coef?cients of their de?ning equations, and this has of course always been known by the classical geometers.
Nevertheless, a correct understanding of what “deforming” means leads into the technically. Equivariant deformations of algebraic varieties with an action of an algebraic torus of complexity 1 RostislavDevyatov.
Abstract Let Xbe a 3-dimensional aﬃne variety with a faithful action of a 2-dimensional torus T. Then the space of ﬁrst order inﬁnitesimal deformations T1(X) is graded by the characters of T,Author: Rostislav Devyatov. sevich ([Ko1], ). See surveys in the book [CKTB]. Poisson Deformations of Algebraic Varieties In algebraic geometry we have to consider deformations as sheaves.
Let Xbe a smooth algebraic variety over K, with structure sheaf OX. We view OX as a Poisson K-algebra with zero bracket. Deﬁnition Deformations of pairs (X, L) Deformations of sections, II Morphisms Deformations of a morphism leaving domain and target fixed Deformations of a morphism leaving the target fixed Morphisms from a nonsingular curve with fixed target Deformations of a closed embedding Versal Property ; Local Deformation Space; Mini-versal deformation space; I came across these words while studying these papers a) Desingularization of moduli varities for vector bundles on curves, Int.
Symp on Algebraic Geometry by C. Seshadri and b) Cohomology of certain moduli spaces of vector bundles Proc. Indian Acad. Sci. by V. Balaji. De nition A G-variety is a variety Xequipped with an action of the algebraic group G: G X. X; (g;x) 7. gx which is also a morphism of varieties.
We then say that is an algebraic G-action. Any algebraic action: G X!Xyields an action of Gon the coordinate ring C[X], via (gf)(x):= f(g 1 x) for all g2G, f2C[X] and x2X.
This action is. Algebraic varieties are the central objects of study in algebraic cally, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition.
The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent sheaves. The global category is very degenerate in general.
Thus, we introduce a new notion of a semi-formal deformation, a Cited by: Pages in category "Algebraic varieties" The following 55 pages are in this category, out of 55 total. This list may not reflect recent changes ().
structed. The deformations are also semiformal, in the sense that the subspace A⊗C[[h]] is closed under the star product. Another approach to the deformation of algebraic varieties is taken in .
It is shown there that any smooth, Poisson algebraic variety (with some topologi-cal requirements) admits a deformation. which is zero since the action of g was a Lie action. For the opposite direction, if V is a representation of Ug, we de ne the action of g by restriction: x(v) = x(v).
This de nes a Lie action since the LHS of () is zero. Remark More conceptually, the assignment g 7!Ug de nes a functor from Lie algebras to associative Size: KB. Abstract. The origin of deformation theory lies in the problem of moduli, first considered by Riemann.
The problem in the theory of moduli can be described thus: to bring together all objects of a single type in analytic geometry, for example, all Riemann surfaces of given genus; to organize them by joining them into a fiber space; to describe the base of this space—the Cited by: 1 A ne Varieties We will begin following Kempf’s Algebraic Varieties, and eventually will do things more like in Hartshorne.
We will also use various sources for commutative algebra. What is algebraic geometry. Classically, it is the study of the zero sets of polynomials. We will now x some notation. kwill be some xed algebraically closed eld. GEOMETRY OF ALGEBRAIC VARIETIES I. Dolgachev and V. Iskovskikh UDC The proposed survey is the third in a series of surveys on algebraic geometry [31, 88].
It is made up mainly from the material in Referativnyi Zhurnal "Matematika" during and is devoted to the geometric aspects of the theory of algebraic varieties. The classical definition of an algebraic variety was limited to affine and projective algebraic sets over the fields of real or complex numbers (cf.
Affine algebraic set; Projective algebraic set). As a result of the studies initiated in the late s by B.L. van der Waerden, E. Noether and others, the concept of an algebraic variety was. This volume contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May at the University of L'Aquila in Italy.
The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. The following work deals with the deformations of embedded affine schemes of codimension 2, which locally have a resolution of length 2.
The cases of immediate interest are curves in 3 Author: Ignacio de Gregorio.The resolution of singular algebraic varieties: Clay Mathematics Institute Summer School, the resolution of singular algebraic varieties, June 3–30,Obergurgl Center, Tyrolean Alps, Austria / David Ellwood, Herwig Hauser, Shigefumi Mori, Josef Schicho, editors.
pages cm. — (Clay mathematics proceedings ; volume 20).Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.
It only takes a minute to sign up. I just started learning computational algebraic geometry so I'm curious. $\endgroup$ – Sergio Parreiras Dec 11 '13 at Topology of product of affine varieties. 1.