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Author: Ingrid C. Bauer Publisher: American Mathematical Soc. ISBN: 0821826891 Category : Mathematics Languages : en Pages : 95
Book Description
The aim of this monograph is the exact description of minimal smooth algebraic surfaces over the complex numbers with the invariants $K DEGREES2 = 7$ und $p_g = 4$. The interest in this fine classification of algebraic surfaces of general type goes back to F. Enriques, who dedicates a large part of his celebrated book Superficie Algebriche to this problem. The cases $p_g = 4$, $K DEGREES2 \leq 6$ were treated in the past by several authors (among others M. Noether, F. Enriques, E. Horikawa) and it is worthwhile to remark that already the case $K DEGREES2 = 6$ is rather complicated and it is up to now not possible to decide whether the moduli space of these surfaces
Author: Ingrid C. Bauer Publisher: American Mathematical Soc. ISBN: 0821826891 Category : Mathematics Languages : en Pages : 95
Book Description
The aim of this monograph is the exact description of minimal smooth algebraic surfaces over the complex numbers with the invariants $K DEGREES2 = 7$ und $p_g = 4$. The interest in this fine classification of algebraic surfaces of general type goes back to F. Enriques, who dedicates a large part of his celebrated book Superficie Algebriche to this problem. The cases $p_g = 4$, $K DEGREES2 \leq 6$ were treated in the past by several authors (among others M. Noether, F. Enriques, E. Horikawa) and it is worthwhile to remark that already the case $K DEGREES2 = 6$ is rather complicated and it is up to now not possible to decide whether the moduli space of these surfaces
Author: Linus Kramer Publisher: American Mathematical Soc. ISBN: 0821829068 Category : Mathematics Languages : en Pages : 137
Book Description
This title classifys 1-connected compact homogeneous spaces which have the same rational cohomology as a product of spheres $\mahtbb{S} DEGREES{n_1}\times\mathbb{S} DEGREES{n_2}$, with $3\leq n_1\leq n_2$ and $n_2$ odd. As an application, it classifys compact generalized quadrangles (buildings of type $C_2)$ which admit a point transitive automorphism group, and isoparametric hypersurfaces which admit a transitive isometry group on one f
Author: Matt Kerr Publisher: Cambridge University Press ISBN: 1316531392 Category : Mathematics Languages : en Pages : 533
Book Description
In its simplest form, Hodge theory is the study of periods – integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.
Author: W. Barth Publisher: Springer ISBN: 3642577393 Category : Mathematics Languages : en Pages : 439
Book Description
In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.
Author: Ingrid Bauer Publisher: Springer Science & Business Media ISBN: 3642562027 Category : Mathematics Languages : en Pages : 357
Book Description
This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday. Hans Grauert is a pioneer in modern complex analysis, continuing the il lustrious German tradition in function theory of several complex variables of Weierstrass, Behnke, Thullen, Stein, Siegel, and many others. When Grauert came on the scene in the early 1950's, function theory was going through a revolutionary period with the geometric theory of complex spaces still in its embryonic stage. A rich theory evolved with the joint efforts of many great mathematicians including Oka, Kodaira, Cartan, and Serre. The Car tan Seminar in Paris and the Kodaira Seminar provided important venues an for its development. Grauert, together with Andreotti and Remmert, took active part in the latter. In his career he has nurtured a great number of his own doctoral students as well as other young mathematicians in his field from allover the world. For a couple of decades his work blazed the trail and set the research agenda in several complex variables worldwide. Among his many fundamentally important contributions, which are too numerous to completely enumerate here, are: 1. The complete clarification of various notions of complex spaces. 2. The solution of the general Levi problem and his work on pseudo convexity for general manifolds. 3. The theory of exceptional analytic sets. 4. The Oka principle for holomorphic bundles. 5. The proof of the Mordell conjecture for function fields. 6. The direct image theorem for coherent sheaves.
Author: Fabrizio Catanese Publisher: Springer Science & Business Media ISBN: 3540354808 Category : Mathematics Languages : en Pages : 508
Book Description
This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry
Author: Roger Chalkley Publisher: American Mathematical Soc. ISBN: 0821827812 Category : Mathematics Languages : en Pages : 223
Book Description
Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.
Author: S. Coen Publisher: Routledge ISBN: 1351445278 Category : Mathematics Languages : en Pages : 522
Book Description
This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry,differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie,B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearch.
Author: Kai Behrend Publisher: American Mathematical Soc. ISBN: 0821829297 Category : Mathematics Languages : en Pages : 110
Book Description
This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
Author: Jeroen Spandaw Publisher: American Mathematical Soc. ISBN: 0821831836 Category : Mathematics Languages : en Pages : 154
Book Description
Studies the cohomology of degeneracy loci. This title assumes that $E\otimes F DEGREES\vee$ is ample and globally generated, and that $\psi$ is a general homomorphism. In order to study the cohomology of $Z$, it considers the Grassmannian bundle $\pi\colon Y: =\mathbb{G}(f-r, F)\to X$ of $(f-r)$-dimensional linear subspaces of the fibre
Author: Ingrid C. Bauer
Author: Ingrid C. Bauer
Author: Linus Kramer
Author: Matt Kerr
Author: W. Barth
Author: Ingrid Bauer
Author: Fabrizio Catanese
Author: Roger Chalkley
Author: S. Coen
Author: Kai Behrend
Author: Jeroen Spandaw