On the Betti numbers of the moduli space of stable bundles of rank two on a curve

1992 ◽  
pp. 92-105 ◽  
Author(s):  
E. Bifet ◽  
F. Ghione ◽  
M. Letizia
Keyword(s):  
Moduli Space ◽  
Betti Numbers ◽  
Stable Bundles

scholarly journals Moduli Spaces of Vector Bundles over a Real Curve: ℤ/2-Betti Numbers

2014 ◽  
Vol 66 (5) ◽  
pp. 961-992 ◽  
Author(s):  
Thomas Baird
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Lagrangian Submanifolds ◽  
Betti Numbers ◽  
Stable Bundles ◽  
Complex Curve ◽  
Yang Mills ◽  
Real Curve

AbstractModuli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi–stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah–Bott's “Yang–Mills over a Riemann Surface” to compute ℤ/2–Betti numbers of these spaces.

scholarly journals Moduli spaces of stable vector bundles on Enriques surfaces

1998 ◽  
Vol 150 ◽  
pp. 85-94 ◽  
Author(s):  
Hoil Kim
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
K3 Surface ◽  
Enriques Surface ◽  
Stable Bundles ◽  
Stable Vector Bundles ◽  
Enriques Surfaces

Abstract.We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.

Moduli of Rank 2 Stable Bundles and Hecke Curves

2016 ◽  
Vol 59 (4) ◽  
pp. 865-877
Author(s):  
Sarbeswar Pal
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Short Note ◽  
Equivalence Classes ◽  
Complex Numbers ◽  
Stable Bundles ◽  
Smooth Projective Curve ◽  
Stable Vector Bundles ◽  
Arbitrary Genus ◽  
Rank 2

AbstractLet X be a smooth projective curve of arbitrary genus g > 3 over the complex numbers. In this short note we will show that the moduli space of rank 2 stable vector bundles with determinant isomorphic to Lx , where Lx denotes the line bundle corresponding to a point x ∊ X, is isomorphic to a certain variety of lines in the moduli space of S-equivalence classes of semistable bundles of rank 2 with trivial determinant.

scholarly journals The Mod Two Cohomology of the Moduli Space of Rank Two Stable Bundles on a Surface and Skew Schur Polynomials

2019 ◽  
Vol 71 (03) ◽  
pp. 683-715 ◽  
Author(s):  
Christopher W. Scaduto ◽  
Matthew Stoffregen
Keyword(s):  
Riemann Surface ◽  
Group Action ◽  
Moduli Space ◽  
Class Group ◽  
Cohomology Ring ◽  
Mapping Class ◽  
Schur Polynomials ◽  
Stable Bundles ◽  
Cohomology Rings ◽  
Cup Product

AbstractWe compute cup-product pairings in the integral cohomology ring of the moduli space of rank two stable bundles with odd determinant over a Riemann surface using methods of Zagier. The resulting formula is related to a generating function for certain skew Schur polynomials. As an application, we compute the nilpotency degree of a distinguished degree two generator in the mod two cohomology ring. We then give descriptions of the mod two cohomology rings in low genus, and describe the subrings invariant under the mapping-class group action.

scholarly journals Stability of the parabolic Poincaré bundle

2018 ◽  
Vol 15 (05) ◽  
pp. 1850081
Author(s):  
Suratno Basu ◽  
Indranil Biswas ◽  
Krishanu Dan
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Compact Riemann Surface ◽  
Stable Bundles ◽  
Parabolic Bundle ◽  
Natural Polarization

Given a compact Riemann surface [Formula: see text] and a moduli space [Formula: see text] of parabolic stable bundles on it of fixed determinant of complete parabolic flags, we prove that the Poincaré parabolic bundle on [Formula: see text] is parabolic stable with respect to a natural polarization on [Formula: see text].

MODULI OF STABLE PAIRS FOR HOLOMORPHIC BUNDLES OVER RIEMANN SURFACES

1991 ◽  
Vol 02 (05) ◽  
pp. 477-513 ◽  
Author(s):  
STEVEN B. BRADLOW ◽  
GEORGIOS D. DASKALOPOULOS
Keyword(s):  
Moduli Space ◽  
Riemann Surfaces ◽  
Holomorphic Section ◽  
Stable Bundles ◽  
Space Problem ◽  
Yang Mills ◽  
Closed Riemann Surface ◽  
Holomorphic Bundles ◽  
Stable Pairs ◽  
Compact Kähler Manifold

It this paper we study the space of gauge equivalence classes of pairs [Formula: see text] where [Formula: see text] represents a holomorphic structure on a complex bundle, E, over a closed Riemann Surface, and ϕ is a holomorphic section. We define a space of stable pairs and consider the moduli space problem for this space. The space of stable pairs, [Formula: see text], is related to the space of solution to the Vortex (Hermitian-Yang-Mills-Higgs) equation. Using the parameter, τ, which appears in this equation we can define subspaces [Formula: see text] within [Formula: see text]. We show that under suitable restrictions on τ and the degree of E, the space [Formula: see text] is naturally a finite dimensional, Hausdorff, compact Kähler manifold. We show further that there is a natural holomorphic map from this space onto the Seshadri compactification of the moduli space of stable bundles and that this map is generically a fibration.

scholarly journals SMALL RATIONAL CURVES ON THE MODULI SPACE OF STABLE BUNDLES

2012 ◽  
Vol 23 (08) ◽  
pp. 1250085 ◽  
Author(s):  
MIN LIU
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Vector Bundles ◽  
Rational Curves ◽  
Projective Curve ◽  
Stable Bundles ◽  
Smooth Projective Curve ◽  
Determinant Formula ◽  
Stable Vector Bundles

For a smooth projective curve C with genus g ≥ 2 and a degree 1 line bundle [Formula: see text] on C, let [Formula: see text] be the moduli space of stable vector bundles of rank r over C with the fixed determinant [Formula: see text]. In this paper, we study the small rational curves on M and estimate the codimension of the locus of the small rational curves. In particular, we determine all small rational curves when r = 3.

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