Singular moduli spaces of rank 2 stable vector bundles

1998 ◽  
Vol 49 (193) ◽  
pp. 31-34
Author(s):  
E Ballico
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Stable Vector Bundles ◽  
Singular Moduli ◽  
Rank 2

scholarly journals RATIONAL FAMILIES OF VECTOR BUNDLES ON CURVES

2004 ◽  
Vol 15 (01) ◽  
pp. 13-45 ◽  
Author(s):  
ANA-MARIA CASTRAVET
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Rational Curves ◽  
Complex Curve ◽  
Stable Vector Bundles ◽  
Irreducible Components ◽  
Rationally Connected ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Let C be a smooth projective complex curve of genus g≥2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k≥1, we find all the irreducible components of the space of rational curves on M, of degree k. In particular, we find the maximal rationally connected fibrations of these components. We prove that there is a one-to-one correspondence between moduli spaces of rational curves on M and moduli spaces of rank 2 vector bundles on ℙ1×C.

scholarly journals VARIATION OF THE GIESEKER AND UHLENBECK COMPACTIFICATIONS

1995 ◽  
Vol 06 (03) ◽  
pp. 397-418 ◽  
Author(s):  
YI HU ◽  
WEI-PING LI
Keyword(s):  
Open Subset ◽  
Moduli Spaces ◽  
Chern Class ◽  
Vector Bundles ◽  
Rational Maps ◽  
Zariski Open Subset ◽  
Stable Vector Bundles ◽  
Rank 2

In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some canonical rational morphisms among the Gieseker compactifications are shown to exist. In particular, we proved that when the second Chern class is sufficiently large, these morphisms are genuine rational maps. Moreover, as a consequence of studying the morphisms from the Gieseker compactifications to the Uhlenbeck compactifications, we show that there is an everywhere-defined canonical algebraic map between two adjacent Uhlenbeck compactifications which restricts to the identity on some Zariski open subset.

scholarly journals THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

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.

scholarly journals EXTENSIONS AND RANK-2 VECTOR BUNDLES ON IRREDUCIBLE NODAL CURVES

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.

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.

Stable vector bundles of rank 2 onP 3

1978 ◽  
Vol 238 (3) ◽  
pp. 229-280 ◽  
Author(s):  
Robin Hartshorne
Keyword(s):  
Vector Bundles ◽  
Stable Vector Bundles ◽  
Rank 2
Sign in / Sign up

Export Citation Format

Share Document