On the rationality of the moduli space for stable rank-2 vector bunoles on P2

1987 ◽  
pp. 363-371 ◽  
Author(s):  
G. Ellingsrud ◽  
S. A. Strømme
Keyword(s):  
Moduli Space ◽  
Stable Rank ◽  
Rank 2

STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS

2003 ◽  
Vol 14 (10) ◽  
pp. 1097-1120 ◽  
Author(s):  
WEI-PING LI ◽  
ZHENBO QIN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Double Cover ◽  
Stable Rank ◽  
Chern Classes ◽  
Canonical Divisor ◽  
Rank 2 ◽  
Stable Sheaves ◽  
Rank 2 Bundles ◽  
Calabi Yau Manifolds

In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

Restriction of Stable Bundles on an Abelian Surface. The C2 = 2 Case

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Cristian Anghel
Keyword(s):  
Moduli Space ◽  
Stable Rank ◽  
Abelian Surface ◽  
Restriction Map ◽  
Stable Bundles ◽  
Genus 2 ◽  
Rank 2 ◽  
Dimension 2 ◽  
Rank 2 Bundles

Abstract In this note we describe the restriction map from the moduli space of stable rank 2 bundles with c2 = 2 on a jacobian X of dimension 2, to the moduli space of stable rank 2 bundles on the corresponding genus 2 curve C embedded in X.

scholarly journals The wobbly divisors of the moduli space of rank-2 vector bundles

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sarbeswar Pal ◽  
Christian Pauly
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Higgs Field ◽  
Picard Group ◽  
Stable Rank ◽  
Complex Curve ◽  
Stable Vector Bundles ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Abstract Let X be a smooth projective complex curve of genus g ≥ 2 and let M X (2,Λ) be the moduli space of semi-stable rank-2 vector bundles over X with fixed determinant Λ. We show that the wobbly locus, i.e. the locus of semi-stable vector bundles admitting a non-zero nilpotent Higgs field, is a union of divisors 𝓦 k ⊂ M X (2,Λ). We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors 𝓦 k in the Picard group of M X (2, Λ).

scholarly journals Generalized null correlation bundles

1988 ◽  
Vol 111 ◽  
pp. 13-24 ◽  
Author(s):  
Lawrence Ein
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Topological Type ◽  
Stable Rank ◽  
Chern Classes ◽  
Smooth Variety ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

It is well known that the moduli space of stable rank 2 vector bundles on ℙ2 of the fixed topological type is an irreducible smooth variety ([1], and [8]). There are also many known results on the classification of stable rank 2 vector bundles on ℙ3 with “small” Chern classes.

ON SINGULARITIES OF ℳℙ3 (c1, c2)

1998 ◽  
Vol 09 (04) ◽  
pp. 407-419 ◽  
Author(s):  
VINCENZO ANCONA ◽  
GIORGIO OTTAVIANI
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Stable Rank ◽  
Chern Classes ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Let ℳℙ3(c1,c2) be the moduli space of stable rank-2 vector bundles on ℙ3 with Chern classes c1, c2. We prove the following results: (1) Let k, β, γ be three integers such that k > 0, 0 ≤ β < γ, γ ≥ 2, kγ - (k + 1)β > 0; then the moduli space ℳℙ3(0, kγ2 - (k + 1)β2) is singular (the case k = 2, β = 0 was previously proved by M. Maggesi). (2) Let k, β, γ be three integers, with β and γ odd, such that k > 0, 0 < β < γ, γ ≥ 5, kγ - (k + 1)β + 1 > 0; then the moduli space ℳℙ3(-1,k(γ/2)2 - (k + 1)(β/2)2) + 1/4) is singular. In particular ℳℙ3(0,5), ℳℙ3(-1,6) are singular.

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.

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