On the Homotopy Groups of Complex Projective Algebraic Manifolds.

Barth, Wolf; Larsen, Mogens Esrom

doi:10.7146/math.scand.a-11066

Cited by 60 publications

(43 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It was an interesting discovery by Barth (see [22][23][24]174] for the following and related results) that a similar (but weaker) result holds true for each smooth subvariety of P N , provided the codimension c = N − n of X is smaller than the dimension.…”

Section: Equivalently the Operator L Given By Cup Product With The Cmentioning

confidence: 99%

Topological methods in moduli theory

Catanese

2015

Bull. Math. Sci.

View full text Add to dashboard Cite

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 classifying spaces, an important class of such varieties is introduced, the one of Bagnera-de Franchis varieties, the quotients of an Abelian variety by the free action of a cyclic group. Moduli spaces of Abelian varieties and of algebraic curves enter into the picture as examples of rational K(H,1)'s, through Teichmüller theory. The main trhust of the paper is to show how in the case of K(H,1)'s the study of moduli spaces and deformation classes can be achieved through by now classical results concerning regularity of classifying maps. The Inoue type varieties of Bauer and Catanese are introduced and studied as a key example, and new results are shown. Motivated from this study, the moduli spaces of algebraic varieties, and especially of algebraic curves with a group of automorphisms of a given topological type are studied in detail, following new results by the author, Michael Lönne and Fabio Perroni. Finally, the action of the absolute Galois group on the moduli spaces of such K(H,1) varieties is studied. In the case of surfaces isogenous to a product, it is shown how this yields a faifhtul action on the set of connected components of the moduli space: for each Galois automorphism of order different from 2 there is an Communicated by Efim Zelmanov.The present work took place in the realm of the DFG Forschergruppe 790 "Classification of algebraic surfaces and compact complex manifolds". Part of the article was written when the author was visiting KIAS, Seoul, as KIAS research scholar.

show abstract

Section: Equivalently the Operator L Given By Cup Product With The Cmentioning

confidence: 99%

Topological methods in moduli theory

Catanese

2015

Bull. Math. Sci.

View full text Add to dashboard Cite

show abstract

“…This in turn was motivated by Barth-Larsen's fundamental result (see [2]) to the effect that smooth varieties X ⊂ P r of low codimension are topologically similar to P r . BarthLarsen's theorem, in our context, can be stated as follows: Theorem 9.2.…”

Section: Speculationsmentioning

confidence: 99%

On the dimension of secant varieties

Chiantini¹,

Ciliberto²

2010

J. Eur. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Part (a) was first proved by Barth [4], using the cohomology of coherent analytic sheaves on P n . Part (c) was proved by Barth and Larsen [5]. Part (b) was proved by Larsen [25], using Morse theory in addition to Barth's earlier techniques.…”

mentioning

confidence: 81%

“…But a surface in P 4 might be a projection of a surface in P 5 . So let us consider a nonsingular surface Y in P 5 , which does not lie in any P 4 . In general, its generic projection into P 4 will have a finite number of double points with transversal tangent planes.…”

Section: and P (\))-+H°(y And Y {\)) Is Surjective Being Linearly Normentioning

confidence: 99%