scholarly journals Nonemptiness of Brill–Noether loci in M(2,L)

2015 ◽  
Vol 26 (13) ◽  
pp. 1550108 ◽  
Author(s):  
H. Lange ◽  
P. E. Newstead ◽  
V. Strehl
Keyword(s):  
Stable Bundles ◽  
Complex Curve ◽  
Fundamental Class ◽  
Determinant Formula ◽  
Combinatorial Lemma ◽  
Odd Degree ◽  
Rank 2 ◽  
Genus Formula

Let [Formula: see text] be a smooth projective complex curve of genus [Formula: see text]. We investigate the Brill–Noether locus consisting of stable bundles of rank 2 and determinant [Formula: see text] of odd degree [Formula: see text] having at least [Formula: see text] independent sections. This locus possesses a virtual fundamental class. We show that in many cases this class is nonzero, which implies that the Brill–Noether locus is nonempty. For many values of [Formula: see text] and [Formula: see text] the result is best possible. We obtain more precise results for [Formula: see text]. Appendix A contains the proof of a combinatorial lemma which we need.

scholarly journals Stable bundles of rank 2 and odd degree over a curve of genus 2

Topology ◽  
1968 ◽  
Vol 7 (3) ◽  
pp. 205-215 ◽  
Author(s):  
P.E. Newstead
Keyword(s):  
Stable Bundles ◽  
Genus 2 ◽  
Odd Degree ◽  
Rank 2

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 line subbundles of stable bundles of rank 2 over an algebraic curve

2007 ◽  
Vol 125 (1) ◽  
pp. 191-202 ◽  
Author(s):  
Insong Choe ◽  
Jaeyoo Choy ◽  
Seongsuk Park
Keyword(s):  
Algebraic Curve ◽  
Stable Bundles ◽  
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 SMALL RATIONAL CURVES ON THE MODULI SPACE OF STABLE BUNDLES

2012 ◽  
Vol 23 (08) ◽  
pp. 1250085 ◽  
Author(s):  
MIN LIU
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Vector Bundles ◽  
Rational Curves ◽  
Projective Curve ◽  
Stable Bundles ◽  
Smooth Projective Curve ◽  
Determinant Formula ◽  
Stable Vector Bundles

For a smooth projective curve C with genus g ≥ 2 and a degree 1 line bundle [Formula: see text] on C, let [Formula: see text] be the moduli space of stable vector bundles of rank r over C with the fixed determinant [Formula: see text]. In this paper, we study the small rational curves on M and estimate the codimension of the locus of the small rational curves. In particular, we determine all small rational curves when r = 3.

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.

Families of vector bundles and linear systems of theta divisors

2017 ◽  
Vol 28 (06) ◽  
pp. 1750039 ◽  
Author(s):  
Sonia Brivio
Keyword(s):  
Linear Systems ◽  
Vector Bundles ◽  
Stable Bundle ◽  
Projective Curve ◽  
Determinant Formula ◽  
Smooth Complex ◽  
Genus Formula ◽  
Semistable Vector Bundles ◽  
Complex Projective ◽  
Complex Projective Curve

Let [Formula: see text] be a smooth complex projective curve of genus [Formula: see text] and let [Formula: see text] be a point. From Hecke correspondence, any stable bundle on [Formula: see text] of rank [Formula: see text] and determinant [Formula: see text] defines a rational family of semistable vector bundles on [Formula: see text] of rank [Formula: see text] and trivial determinant. In this paper, we study linear systems of theta divisors associated to these families.

scholarly journals Hecke cycles associated to rank 2 twisted Higgs bundles on a curve

2019 ◽  
Vol 30 (12) ◽  
pp. 1950062
Author(s):  
Sang-Bum Yoo
Keyword(s):  
Moduli Space ◽  
Rational Maps ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Complex ◽  
Rank 2 ◽  
Genus Formula ◽  
Hecke Modifications ◽  
Complex Projective ◽  
Complex Projective Curve

Let [Formula: see text] be a smooth complex projective curve of genus [Formula: see text] and let [Formula: see text] be a line bundle on [Formula: see text] with [Formula: see text]. Let [Formula: see text] be the moduli space of semistable rank 2 [Formula: see text]-twisted Higgs bundles with trivial determinant on [Formula: see text]. Let [Formula: see text] be the moduli space of stable rank 2 [Formula: see text]-twisted Higgs bundles with determinant [Formula: see text] for some [Formula: see text] on [Formula: see text]. We construct a cycle in the product of a stack of rational maps from nonsingular curves to [Formula: see text] and [Formula: see text] by using Hecke modifications of a stable [Formula: see text]-twisted Higgs bundle in [Formula: see text].

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