Inoue type manifolds and Inoue surfaces: a connected component of the moduli space of surfaces with K2 = 7, pg = 0

2012 ◽  
pp. 23-56 ◽  
Author(s):  
Ingrid Bauer ◽  
Fabrizio Catanese
Keyword(s):  
Moduli Space ◽  
Connected Component ◽  
Inoue Surfaces

scholarly journals A connected component of the moduli space of surfaces with pg=0

Topology ◽  
2001 ◽  
Vol 40 (5) ◽  
pp. 977-991 ◽  
Author(s):  
Margarida Mendes Lopes ◽  
Rita Pardini
Keyword(s):  
Moduli Space ◽  
Connected Component

scholarly journals Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

2021 ◽  
Author(s):  
Fabian Reede ◽  
Ziyu Zhang
Keyword(s):  
Moduli Space ◽  
Hilbert Scheme ◽  
Vector Bundles ◽  
K3 Surfaces ◽  
Hilbert Schemes ◽  
Connected Component ◽  
Stable Vector Bundles ◽  
Universal Family ◽  
Hilbert Scheme Of Points ◽  
Flat Family

AbstractLet X be a projective K3 surfaces. In two examples where there exists a fine moduli space M of stable vector bundles on X, isomorphic to a Hilbert scheme of points, we prove that the universal family $${\mathcal {E}}$$ E on $$X\times M$$ X × M can be understood as a complete flat family of stable vector bundles on M parametrized by X, which identifies X with a smooth connected component of some moduli space of stable sheaves on M.

Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Indranil Biswas ◽  
Amit Hogadi ◽  
Yogish Holla
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Projective Variety ◽  
Brauer Group ◽  
Projective Curve ◽  
Connected Component ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Complex Projective ◽  
Complex Projective Curve

AbstractLet X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.

scholarly journals The algebra of cell-zeta values

2010 ◽  
Vol 146 (3) ◽  
pp. 731-771 ◽  
Author(s):  
Francis Brown ◽  
Sarah Carr ◽  
Leila Schneps
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Cohomology Group ◽  
Differential Forms ◽  
Natural Duality ◽  
Connected Component ◽  
Real Numbers ◽  
Zeta Values ◽  
Definition Of ◽  
Formal Version

AbstractIn this paper, we introduce cell-forms on 𝔐0,n, which are top-dimensional differential forms diverging along the boundary of exactly one cell (connected component) of the real moduli space 𝔐0,n(ℝ). We show that the cell-forms generate the top-dimensional cohomology group of 𝔐0,n, so that there is a natural duality between cells and cell-forms. In the heart of the paper, we determine an explicit basis for the subspace of differential forms which converge along a given cell X. The elements of this basis are called insertion forms; their integrals over X are real numbers, called cell-zeta values, which generate a ℚ-algebra called the cell-zeta algebra. By a result of F. Brown, the cell-zeta algebra is equal to the algebra of multizeta values. The cell-zeta values satisfy a family of simple quadratic relations coming from the geometry of moduli spaces, which leads to a natural definition of a formal version of the cell-zeta algebra, conjecturally isomorphic to the formal multizeta algebra defined by the much-studied double shuffle relations.

scholarly journals ON TYPICALITY OF TRANSLATION FLOWS WHICH ARE DISJOINT WITH THEIR INVERSE

2018 ◽  
Vol 19 (5) ◽  
pp. 1677-1737
Author(s):  
Przemysław Berk ◽  
Krzysztof Frączek ◽  
Thierry de la Rue
Keyword(s):  
Moduli Space ◽  
Dense Subset ◽  
Vertical Flow ◽  
Connected Component ◽  
Continuous Embedding ◽  
Vertical Translation

In this paper we prove that the set of translation structures for which the corresponding vertical translation flows are disjoint with its inverse contains a $G_{\unicode[STIX]{x1D6FF}}$-dense subset in every non-hyperelliptic connected component of the moduli space ${\mathcal{M}}$. This is in contrast to hyperelliptic case, where for every translation structure the associated vertical flow is reversible, i.e., it is isomorphic to its inverse by an involution. To prove the main result, we study limits of the off-diagonal 3-joinings of special representations of vertical translation flows. Moreover, we construct a locally defined continuous embedding of the moduli space into the space of measure-preserving flows to obtain the $G_{\unicode[STIX]{x1D6FF}}$-condition. Moreover, as a by-product we get that in every non-hyperelliptic connected component of the moduli space there is a dense subset of translation structures whose vertical flow is reversible.

scholarly journals Kulikov surfaces form a connected component of the moduli space

2013 ◽  
Vol 210 ◽  
pp. 1-27 ◽  
Author(s):  
Tsz On Mario Chan ◽  
Stephen Coughlan
Keyword(s):  
Moduli Space ◽  
General Type ◽  
Connected Component ◽  
Surfaces Of General Type

AbstractWe show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type with pg = 0 and K2 = 6. We also give a new description for these surfaces, extending ideas of Inoue. Finally, we calculate the bicanonical degree of Kulikov surfaces and prove that they verify the Bloch conjecture.

scholarly journals Kulikov surfaces form a connected component of the moduli space

2013 ◽  
Vol 210 ◽  
pp. 1-27
Author(s):  
Tsz On Mario Chan ◽  
Stephen Coughlan
Keyword(s):  
Moduli Space ◽  
General Type ◽  
Connected Component ◽  
Surfaces Of General Type

AbstractWe show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type withpg= 0 andK2= 6. We also give a new description for these surfaces, extending ideas of Inoue. Finally, we calculate the bicanonical degree of Kulikov surfaces and prove that they verify the Bloch conjecture.

Topology of the quantum modified moduli space

2001 ◽  
Vol 15 (4) ◽  
pp. 279-289
Author(s):  
S. L. Dubovsky
Keyword(s):  
Moduli Space

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

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