Smooth structures on algebraic surfaces with cyclic fundamental group

1988 ◽  
Vol 91 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Ian Hambleton ◽  
Matthias Kreck
Keyword(s):  
Fundamental Group ◽  
Algebraic Surfaces ◽  
Smooth Structures

Smooth structures on algebraic surfaces with finite fundamental group

1990 ◽  
Vol 102 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Ian Hambleton ◽  
Matthias Kreck
Keyword(s):  
Fundamental Group ◽  
Algebraic Surfaces ◽  
Smooth Structures ◽  
Finite Fundamental Group

scholarly journals Twisted Donaldson invariants

2021 ◽  
pp. 1-54
Author(s):  
TSUYOSHI KATO ◽  
HIROFUMI SASAHIRA ◽  
HANG WANG
Keyword(s):  
Gauge Theory ◽  
Fundamental Group ◽  
Picard Group ◽  
Fundamental Groups ◽  
Smooth Structure ◽  
Yang Mills ◽  
Smooth Structures ◽  
New Variant ◽  
Donaldson Invariants

Abstract Fundamental group of a manifold gives a deep effect on its underlying smooth structure. In this paper we introduce a new variant of the Donaldson invariant in Yang–Mills gauge theory from twisting by the Picard group of a 4-manifold in the case when the fundamental group is free abelian. We then generalise it to the general case of fundamental groups by use of the framework of non commutative geometry. We also verify that our invariant distinguishes smooth structures between some homeomorphic 4-manifolds.

scholarly journals Fundamental group of Galois covers of degree 6 surfaces

2021 ◽  
pp. 1-21
Author(s):  
M. Amram ◽  
C. Gong ◽  
U. Sinichkin ◽  
S.-L. Tan ◽  
W.-Y. Xu ◽  
...  
Keyword(s):  
Fundamental Group ◽  
Algebraic Surfaces ◽  
Fundamental Groups ◽  
Galois Cover ◽  
Chern Numbers ◽  
Galois Covers

In this paper, we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations, the fundamental group of the Galois cover is non-trivial and for 20 types it is trivial. Moreover, we compute the Chern numbers of all the surfaces with this type of degeneration and prove that the signatures of all their Galois covers are negative. We formulate a conjecture regarding the structure of the fundamental groups of the Galois covers based on our findings.

Invariant groups associated with an algebraic surface

1940 ◽  
Vol 36 (4) ◽  
pp. 414-423 ◽  
Author(s):  
D. B. Scott
Keyword(s):  
Fundamental Group ◽  
Algebraic Curve ◽  
Algebraic Surface ◽  
Algebraic Surfaces ◽  
Topological Invariants ◽  
Period Matrix ◽  
Birational Transformations

Alexander (1, 2) has introduced certain topological invariants of a manifold which arise from the intersections of cycles of non-complementary dimensions, and he points out that they are not derivable from the Betti and torsion numbers, nor from the fundamental group. In the present paper we consider some topological invariants of this type on an algebraic surface, and, although we cannot define them completely, we show that they are intimately connected with the multiplications of the period matrix of the simple integrals of the first kind. We are then led to a concept which we call the “intersection group” of the surface, which is, by its definition, topologically invariant, and we show that it is also invariant under birational transformations. The proofs are based on Lefschetz's theory of cycles for an algebraic surface (4) and some simple properties of the period matrix of an algebraic curve. The results obtained here have a number of applications to the theory of ∞3 correspondences between algebraic surfaces, as we propose to show in a later paper.

Complex Algebraic Surfaces

1996 ◽  
Author(s):  
Arnaud Beauville
Keyword(s):  
Algebraic Surfaces

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

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