Topological methods in algebraic geometry

  title={Topological methods in algebraic geometry},
  author={Fabrizio M.E. Catanese},
Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1. Applications of algebraic topology: non existence and existence of continuous maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2. Projective varieties which are K (π, 1) . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.1 Rational K (π, 1)’s: basic examples . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. Regularity of classifying maps and… 
Hodge-Deligne polynomials of character varieties of free abelian groups
Abstract Let F F be a finite group and X X be a complex quasi-projective F F -variety. For r ∈ N r\in {\mathbb{N}} , we consider the mixed Hodge-Deligne polynomials of quotients X r / F
Local polar varieties in the geometric study of singularities
This text presents several aspects of the theory of equisingularity of complex analytic spaces from the standpoint of Whitney conditions. The goal is to describe from the geometrical, topological,
Motivic Chern classes of Schubert cells, Hecke algebras, and applications to Casselman's problem
Motivic Chern classes are elements in the K-theory of an algebraic variety $X$ depending on an extra parameter $y$. They are determined by functoriality and a normalization property for smooth $X$.
Characteristic Classes
  • A. Ranicki
  • Mathematics
    Lectures on the Geometry of Manifolds
  • 2020
The goal of this lecture notes is to introduce to Characteristic Classes. This is an important tool of the contemporary mathematics, indispensable to work in geometry and topology, and also useful in
Topology through the centuries: Low dimensional manifolds
This note will provide a lightning tour through the centuries, concentrating on the study of manifolds of dimension 2, 3, and 4. Further comments and more technical details about many of the sections
Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-K\"ahler manifolds
We prove that the complex cobordism class of any hyper-Kähler manifold of dimension 2n is a unique combination with rational coefficients of classes of products of punctual Hilbert schemes of K3
Todd genus and $A_k$-genus of unitary $S^1$-manifolds
J : TM ⊕ R −→ TM ⊕ R such that J = −1, where R denotes the trivial real l-plane bundle over M for some l. A stable complex structure induces an orientation, obtained as the “difference” of the
Some Fano manifolds whose Hilbert polynomial is totally reducible over $\mathbb Q$
Let (X,L) be any Fano manifold polarized by a positive multiple of its fundamental divisor H . The polynomial defining the Hilbert curve of (X,L) boils down to being the Hilbert polynomial of (X,H),
Sheaf Theory for Partial Differential Equations
In order to analyze the singularities of hyperfunction solutions of systems of partial differential equations, M. Sato introduced in 1969 the microlocalization functor and, more fundamentally, the


Compact complex surfaces.
Historical Note.- References.- The Content of the Book.- Standard Notations.- I. Preliminaries.- Topology and Algebra.- 1. Notations and Basic Facts.- 2. Some Properties of Bilinear forms.- 3. Vector
Lectures on Algebraic Topology
I Preliminaries on Categories, Abelian Groups, and Homotopy.- x1 Categories and Functors.- x2 Abelian Groups (Exactness, Direct Sums, Free Abelian Groups).- x3 Homotopy.- II Homology of Complexes.-
Topological methods in moduli theory
One of the main themes of this long article is the study of projective varieties which are K(H,1)’s, i.e. classifying spaces BH for some discrete group H. After recalling the basic properties of such
Rational Homotopy Theory and Differential Forms
1 Introduction.- 2 Basic Concepts.- 3 CW Homology Theorem.- 4 The Whitehead Theorem and the Hurewicz Theorem.- 5 Spectral Sequence of a Fibration.- 6 Obstruction Theory.- 7 Eilenberg-MacLane Spaces,
Strong Rigidity of Locally Symmetric Spaces.
*Frontmatter, pg. i*Contents, pg. v* 1. Introduction, pg. 1* 2. Algebraic Preliminaries, pg. 10* 3. The Geometry of chi : Preliminaries, pg. 20* 4. A Metric Definition of the Maximal Boundary, pg.
Arakelov inequalities and the uniformization of certain rigid Shimura varieties
Let Y be a non-singular projective manifold with an ample canonical sheaf, and let V be a Q-variation of Hodge structures of weight one on Y with Higgs bundle E 1,0 ⊕ E 0,1 , coming from a family of
Fibred Kähler and quasi-projective groups.
We formulate a new theorem giving several necessary and sufficient conditions in order that a surjection of the fundamental group πι^) of a compact Kahler manifold onto the fundamental group Π^ of a
Fibred surfaces, varieties isogenous to a product and related moduli spaces
A fibration of an algebraic surface S over a curve B, with fibres of genus at least 2, has constant moduli iff it is birational to the quotient of a product of curves by the action of a finite group
Surfaces and the second homology of a group
LetG be a group andK(G, 1) an Eilenberg—MacLane space, i.e. π1(K(G,1))≅G, πi(K(G,1))=0,i≠1. We give a purely algebraic proof that the second homology groupH2(G)=H2(G,ℤ)≅H2(K(G,1)) is isomorphic to
On the moduli spaces of surfaces of general type
It is nowadays well known that there exists a coarse moduli space Wl for complete smooth curves of genus g, and that Wlg is a quasiprojective normal irreducible variety of dimension 3g — 3. Recently