Download The Geometry of Moduli Spaces of Sheaves: A Publication of by Dr. Daniel Huybrechts, Dr. Manfred Lehn (auth.) PDF

By Dr. Daniel Huybrechts, Dr. Manfred Lehn (auth.)

Diese Monographie gibt eine Einführung in ein aktuelles Teilgebiet der Algebraischen Geometrie: Die Theorie der Modulräume für Vektorbündel und kohärente Garben hat sich in der letzten Zeit in vielen Richtungen entwickelt und findet Interesse in zahlreichen mathematischen Zentren, z. B. in Bonn oder an der Harvard collage, USA.

Introduction - Preliminaries - households of Sheaves - The Grauert-Mülich Theorem - Moduli areas - building equipment - Moduli areas on K3 Surfaces - restrict of Sheaves to Curves - Line Bundles at the Moduli house - Irreducibility and Smoothness - Symplectic constructions - Birational Properties

Diplomstudenten höherer Semester und Mathematiker an Universitäten, Institute, Bibliotheken

Über den Autor/Hrsg
Dr. Huybrechts forscht an der Humboldt Universität Berlin und Dr. Lehn an der Universität Bielefeld.

Show description

Read or Download The Geometry of Moduli Spaces of Sheaves: A Publication of the Max-Planck-Institut für Mathematik, Bonn PDF

Similar geometry books

The Pythagorean Theorem: Crown Jewel of Mathematics

The Pythagorean Theorem, Crown Jewel of arithmetic chronologically strains the Pythagorean Theorem from a conjectured starting, examine the Squares (Chapter 1), via 4000 years of Pythagorean proofs, 4 Thousand Years of Discovery (Chapter 2), from all significant facts different types, 20 proofs in overall.

K-theory and noncommutative geometry

On account that its inception 50 years in the past, K-theory has been a device for figuring out a wide-ranging kin of mathematical buildings and their invariants: topological areas, jewelry, algebraic types and operator algebras are the dominant examples. The invariants diversity from attribute sessions in cohomology, determinants of matrices, Chow teams of types, in addition to strains and indices of elliptic operators.

Real Algebraic Geometry and Ordered Structures: Ams Special Session on Real Algebraic Geometry and Ordered Algebraic Structures Held at Louisiana ... April 17-21, 1996

This quantity includes sixteen conscientiously refereed articles by way of members within the detailed consultation on genuine Algebraic Geometry and Ordered Algebraic buildings on the Sectional assembly of the AMS in Baton Rouge, April 1996, and the linked unique Semester within the spring of 1996 at Louisiana country collage and Southern college, Baton Rouge.

Topics in Ergodic Theory.

This booklet issues parts of ergodic idea which are now being intensively constructed. the themes comprise entropy concept (with emphasis on dynamical structures with multi-dimensional time), components of the renormalization staff approach within the conception of dynamical structures, splitting of separatrices, and a few difficulties with regards to the speculation of hyperbolic dynamical platforms.

Additional info for The Geometry of Moduli Spaces of Sheaves: A Publication of the Max-Planck-Institut für Mathematik, Bonn

Example text

Pi=: Pmin(E). Obviously, E is semistable if and only if E is pure andpmax(E) = Pmin(E). A priori, the definition of the maximal and minimal p of a sheaf E depends on the filtration. We will see in the next theorem, that the Harder-Narasimhan filtration is uniquely determined, so that there is no ambiguity in the notation. 3 -IfF and G are pure sheaves of dimension d with Pmin(F) then Hom(F, G)= 0. > Pmax(G), Proof Suppose 'lj; : F -+ G is non-trivial. Let i > 0 be minimal with 'lj;(HN;(F)) =f 0 and let j > 0 be minimal with 'lj;(HN;(F)) C HNj(G)).

Choosing a closed immersion i : X -+ lP'~ and replacing 1i by i* 1i we may reduce to the case X = lP'~. By Serre's theorem there exist presentations OpN( -m"t" ----+ OpN( -m't' ----+ 1i----+ 0. 3 any quotient of 1i can be considered as a quotient of OpN . T ( -m')n'. Conversely, a quotient F of OpN( -m')n' factors through ti, if and only if the composite T homomorphism OpN( -m")n" -+ OpN( -m')n' -+ F vanishes. ) for some k sufficiently large integer £.. f/k(O( -m')n', P). D Since Q := Quotx;s(ti, P) represents the functor Q ·- Quotx15 (1i, P), we have Mor(Sch/S) (Y, Q) = Q(Y) for any S-scheme Y.

2). 1 Flat Families and Determinants Let f : X -+ S be a morphism of finite type of Noetherian schemes. If g : T -+ Sis an Sscheme we will use the notation X T for the fibre product T x s X, and g x : X T -+ X and h: Xr-+ T for the natural projections. ForsE S the fibre f- 1 (s) = Spec(k(s)) Xs X is denoted X 8 • Similarly, ifF is a coherent Ox-module, we write Fr := g'XF and Fs = Fix•. Often, we will think ofF as a collection of sheaves Fs parametrized by s E S. 1 -A fiat family of coherent sheaves on the fibres off is a coherent 0 xmodule F which is fiat overS.

Download PDF sample

Rated 4.77 of 5 – based on 11 votes