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 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 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.

Maximal Subbundles of Rank 2 Vector Bundles on Projective Curves

2000 ◽  
Vol 43 (2) ◽  
pp. 129-137 ◽  
Author(s):  
E. Ballico
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Stable Rank ◽  
Maximal Degree ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Stable Vector Bundles ◽  
Projective Curves ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

AbstractLet E be a stable rank 2 vector bundle on a smooth projective curve X and V(E) be the set of all rank 1 subbundles of E with maximal degree. Here we study the varieties (non-emptyness, irreducibility and dimension) of all rank 2 stable vector bundles, E, on X with fixed deg(E) and deg(L), L ∈ V(E) and such that .

scholarly journals Stable vector bundles on quadric hypersurfaces

1984 ◽  
Vol 96 ◽  
pp. 11-22 ◽  
Author(s):  
L. Ein ◽  
I. Sols
Keyword(s):  
Vector Bundles ◽  
Stable Rank ◽  
Vanishing Theorem ◽  
Restriction Theorem ◽  
Stable Vector Bundles ◽  
Rational Varieties ◽  
Rank 2 ◽  
Rank 2 Vector Bundles ◽  
Definition Of ◽  
Rank 2 Bundles

Barth, Hulek and Maruyama have showed that the moduli of stable rank 2 vector bundles on P2 are nonsingular rational varieties. There are also many examples of stable rank 2 vector bundles on P3. On the other hand, there is essentially only one example of rank 2 bundles on P4, which is constructed by Horrocks and Mumford. We hope the study of rank 2 bundles on hypersurfaces in P4 may give more insight to the study of vector bundles on P4. In this paper, we establish some general properties of stable rank 2 bundles on quadric hypersurfaces. We show the restriction theorem (1.4), (1.6), the existence of the spectrum (2.2), and the vanishing theorem (2.4), are also true for the stable rank 2 reflexive sheaves on quadric hypersurfaces just as in the case when the base variety is Pn. Though the methods to prove such results are similar to those we use for projective spaces, there are some technical difficulties. We should also mention that we shall always assume the base field is characteristic 0 and algebraically closed, and we shall use the definition of stability introduced by Mumford and Takemoto.

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.

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.

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