Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the semistability of certain Lazarsfeld–Mukai bundles on abelian surfaces

On the semistability of certain Lazarsfeld–Mukai bundles on abelian surfaces Let $$X=\mathscr {J}(\widetilde{\mathscr {C}})$$ X = J ( C ~ ) , the Jacobian of a genus 2 curve $$\widetilde{\mathscr {C}}$$ C ~ over $${\mathbb {C}}$$ C , and let Y be the associated Kummer surface. Consider an ample line bundle $$L=\mathscr {O}(m\widetilde{\mathscr {C}})$$ L = O ( m C ~ ) on X for an even number m, and its descent to Y, say $$L'$$ L ′ . We show that any dominating component of $${\mathscr {W}}^1_{d}(|L'|)$$ W d 1 ( | L ′ | ) corresponds to $$\mu _{L'}$$ μ L ′ -stable Lazarsfeld–Mukai bundles on Y. Further, for a smooth curve $$C\in |L|$$ C ∈ | L | and a base-point free $$g^1_d$$ g d 1 on C, say (A, V), we study the $$\mu _L$$ μ L -semistability of the rank-2 Lazarsfeld–Mukai bundle associated to (C, (A, V)) on X. Under certain assumptions on C and the $$g^1_d$$ g d 1 , we show that the above Lazarsfeld–Mukai bundles are $$\mu _L$$ μ L -semistable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

On the semistability of certain Lazarsfeld–Mukai bundles on abelian surfaces

Download PDF
20 pages

Loading next page...
 
/lp/springer-journals/on-the-semistability-of-certain-lazarsfeld-mukai-bundles-on-abelian-YMQWNKTZQx
Publisher
Springer Journals
Copyright
Copyright © 2017 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-017-0277-z
Publisher site
See Article on Publisher Site

Abstract

Let $$X=\mathscr {J}(\widetilde{\mathscr {C}})$$ X = J ( C ~ ) , the Jacobian of a genus 2 curve $$\widetilde{\mathscr {C}}$$ C ~ over $${\mathbb {C}}$$ C , and let Y be the associated Kummer surface. Consider an ample line bundle $$L=\mathscr {O}(m\widetilde{\mathscr {C}})$$ L = O ( m C ~ ) on X for an even number m, and its descent to Y, say $$L'$$ L ′ . We show that any dominating component of $${\mathscr {W}}^1_{d}(|L'|)$$ W d 1 ( | L ′ | ) corresponds to $$\mu _{L'}$$ μ L ′ -stable Lazarsfeld–Mukai bundles on Y. Further, for a smooth curve $$C\in |L|$$ C ∈ | L | and a base-point free $$g^1_d$$ g d 1 on C, say (A, V), we study the $$\mu _L$$ μ L -semistability of the rank-2 Lazarsfeld–Mukai bundle associated to (C, (A, V)) on X. Under certain assumptions on C and the $$g^1_d$$ g d 1 , we show that the above Lazarsfeld–Mukai bundles are $$\mu _L$$ μ L -semistable.

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Mar 10, 2017

References

  • Green’s conjecture for curves on arbitrary K3 surfaces
    Aprodu, M; Farkas, G
  • Complex Algebraic Surfaces
    Beauville, A
  • Some stable vector bundles with reducible theta divisor
    Beauville, A
  • Complex Abelian Varieties
    Birkenhake, C; Lange, H
  • Normal generation of vector bundles over a curve
    Butler, D
  • About the stability of the tangent bundle of $${\mathbb{P}}^n$$ P n restricted to a curve
    Camere, C
  • About the stability of the tangent bundle of $${\mathbb{P}}^n$$ P n restricted to a surface
    Camere, C
  • Linear systems on K3-sections
    Donagi, R; Morrison, DR
  • Stability and restrictions of Picard bundles, with an application to the normal bundles of elliptic curves, Complex Projective Geometry
    Ein, L; Lazarsfeld, R
  • Stability of syzygy bundles on an algebraic surface
    Ein, L; Lazarsfeld, R; Mustopa, Y
  • The Clifford dimension of a projective curve
    Eisenbud, D; Lange, H; Martens, G; Schreyer, F-O
  • Restrictions of semistable bundles on projective varieties
    Flenner, H
  • Algebraic Geometry, Graduate Texts in Mathematics
    Hartshorne, R
  • The Geometry of Moduli Spaces of Sheaves
    Huybrechts, D; Lehn, M
  • On two conjectures for curves on K3 surfaces
    Knutsen, AL
  • Lectures on Vector Bundles, Cambridge Studies in Advanced Mathematics
    Potier, J
  • The theorem of Grauert-Mülich-Spindler
    Maruyama, M
  • Stability of line bundle transforms on curves with respect to low codimensional subspaces
    Mistretta, E
  • On the equations defining abelian varieties I
    Mumford, D
  • On the Canonical Ring of a Curve, Algebraic Geometry and Commutative Algebra, Volume II
    Paranjape, K; Ramanan, S