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

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.

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.

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 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.

Quadratic complexes. II

1982 ◽  
Vol 91 (2) ◽  
pp. 183-206 ◽  
Author(s):  
P. E. Newstead
Keyword(s):  
Vector Bundles ◽  
Quadratic Equation ◽  
Stable Vector Bundles ◽  
Algebraic Vector ◽  
Universal Family ◽  
Quadric Cone ◽  
Genus 2 ◽  
Rank 2 ◽  
Pass Through ◽  
Dimensional Projective Space

A quadratic complex Q is the set of lines in 3-dimensional projective space 3 given by a single non-trivial quadratic equation in the Plücker coordinates. The lines of the complex which pass through a fixed point of 3 are, in general, the generators of a quadric cone; this cone degenerates for the points of a sub variety K of 3. Thus one can associate with Q a fibration with base 3 - K and fibre isomorphic to 1, and ask whether this fibration is associated with an algebraic vector bundle of rank 2. When the base field is and Q is non-singular, the answer is negative; this was proved some years ago by Narasimhan and Ramanan ((8), proposition 8·1), and has the consequence that there is no universal family of stable vector bundles of rank 2 and degree 0 over a curve of genus 2.

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 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.

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