Hecke curves on the moduli space of vector bundles over an algebraic curve

AbstractWe prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism $\mathcal {M}_{\mathbf {O}_r} \longrightarrow \mathcal {M}_{\mathbf {GL}_r}$ (respectively $\mathcal M_{\mathbf {Sp}_{2r}}\longrightarrow \mathcal M_{\mathbf {GL}_{2r}}$) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.

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The moduli space of stable vector bundles over a real algebraic curve

Mathematische Annalen ◽

10.1007/s00208-009-0442-5 ◽

2009 ◽

Vol 347 (1) ◽

pp. 201-233 ◽

Cited By ~ 21

Author(s):

Indranil Biswas ◽

Johannes Huisman ◽

Jacques Hurtubise

Keyword(s):

Moduli Space ◽

Algebraic Curve ◽

Vector Bundles ◽

Stable Vector Bundles ◽

Real Algebraic Curve

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Deformations of the Moduli Space of Vector Bundles Over an Algebraic Curve

Annals of Mathematics ◽

10.2307/1970933 ◽

1975 ◽

Vol 101 (3) ◽

pp. 391 ◽

Cited By ~ 60

Author(s):

M. S. Narasimhan ◽

S. Ramanan

Keyword(s):

Moduli Space ◽

Algebraic Curve ◽

Vector Bundles

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On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve

manuscripta mathematica ◽

10.1007/s00229-013-0618-x ◽

2013 ◽

Vol 142 (3-4) ◽

pp. 525-544 ◽

Cited By ~ 1

Author(s):

L. Brambila-Paz ◽

O. Mata-Gutiérrez

Keyword(s):

Moduli Space ◽

Hilbert Scheme ◽

Algebraic Curve ◽

Vector Bundles

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THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

Nagoya Mathematical Journal ◽

10.1017/nmj.2020.37 ◽

2020 ◽

pp. 1-23

Author(s):

MICHELE BOLOGNESI ◽

NÉSTOR FERNÁNDEZ VARGAS

Keyword(s):

Moduli Space ◽

Moduli Spaces ◽

Vector Bundles ◽

Hyperelliptic Curve ◽

Geometric Description ◽

Birational Model ◽

Rank 2 ◽

Semistable Vector Bundles ◽

Ramification Locus

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

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EXTENSIONS AND RANK-2 VECTOR BUNDLES ON IRREDUCIBLE NODAL CURVES

International Journal of Mathematics ◽

10.1142/s0129167x05003284 ◽

2005 ◽

Vol 16 (10) ◽

pp. 1081-1118

Author(s):

D. ARCARA

Keyword(s):

Moduli Space ◽

Vector Bundles ◽

Rational Map ◽

Nodal Curves ◽

Nodal Curve ◽

Stable Vector Bundles ◽

Rank 2 ◽

Rank 2 Vector Bundles

We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use the natural rational map [Formula: see text] defined by [Formula: see text] to study a compactification [Formula: see text] of the moduli space [Formula: see text] of semi-stable vector bundles of rank 2 and determinant L on C. In particular, we resolve the indeterminancy of ϕL in the case deg L = 3,4 via a sequence of three blow-ups with smooth centers.

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