On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors

Alina Marian[1]; Dragos Oprea[2]

  • [1] Northeastern University Department of Mathematics 567 Lake Hall Boston, MA 02115 (USA)
  • [2] University of California Department of Mathematics 9500 Gilman Drive ♯ 0112 La Jolla, CA 92093-0112 (USA)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 5, page 2067-2086
  • ISSN: 0373-0956

Abstract

top
We extend results on generic strange duality for K 3 surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized K 3 s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized K 3 s .

How to cite

top

Marian, Alina, and Oprea, Dragos. "On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors." Annales de l’institut Fourier 64.5 (2014): 2067-2086. <http://eudml.org/doc/275519>.

@article{Marian2014,
abstract = {We extend results on generic strange duality for $K3$ surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized $K3$s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized $K3s$.},
affiliation = {Northeastern University Department of Mathematics 567 Lake Hall Boston, MA 02115 (USA); University of California Department of Mathematics 9500 Gilman Drive ♯ 0112 La Jolla, CA 92093-0112 (USA)},
author = {Marian, Alina, Oprea, Dragos},
journal = {Annales de l’institut Fourier},
keywords = {$K$3 surface; moduli space of sheaves; strange duality; surface},
language = {eng},
number = {5},
pages = {2067-2086},
publisher = {Association des Annales de l’institut Fourier},
title = {On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors},
url = {http://eudml.org/doc/275519},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Marian, Alina
AU - Oprea, Dragos
TI - On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 5
SP - 2067
EP - 2086
AB - We extend results on generic strange duality for $K3$ surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized $K3$s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized $K3s$.
LA - eng
KW - $K$3 surface; moduli space of sheaves; strange duality; surface
UR - http://eudml.org/doc/275519
ER -

References

top
  1. W. Barth, C. Peters, A. Van de Ven, Compact complex surfaces, 4 (1984), Springer-Verlag, Berlin Zbl1036.14016MR749574
  2. M. Bernardara, G. Hein, The Euclid-Fourier-Mukai algorithm for elliptic surfaces Zbl1311.14044
  3. Tom Bridgeland, Fourier-Mukai transforms for elliptic surfaces, J. Reine Angew. Math. 498 (1998), 115-133 Zbl0905.14020MR1629929
  4. Andrei Horia Caldararu, Derived categories of twisted sheaves on Calabi-Yau manifolds, (2000), ProQuest LLC, Ann Arbor, MI MR2700538
  5. Geir Ellingsrud, Lothar Göttsche, Manfred Lehn, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001), 81-100 Zbl0976.14002MR1795551
  6. Robert Friedman, Algebraic surfaces and holomorphic vector bundles, (1998), Springer-Verlag, New York Zbl0902.14029MR1600388
  7. Gerard van der Geer, Toshiyuki Katsura, Note on tautological classes of moduli of K 3 surfaces, Mosc. Math. J. 5 (2005), 775-779, 972 Zbl1124.14011MR2266459
  8. D. Hernandez Ruiperez, A. C. Lopez Martin, F. Sancho de Salas, Relative integral functors for singular fibrations and singular partners, J. Eur. Math. Soc. 11 (2009), 597-625 Zbl1221.18010MR2505443
  9. Daniel Huybrechts, Birational symplectic manifolds and their deformations, J. Differential Geom. 45 (1997), 488-513 Zbl0917.53010MR1472886
  10. J. Le Potier, Fibré déterminant et courbes de saut sur les surfaces algébriques, Complex projective geometry (Trieste, 1989/Bergen, 1989) 179 (1992), 213-240, Cambridge Univ. Press, Cambridge Zbl0788.14045MR1201385
  11. J. Le Potier, Dualité étrange sur le plan projectif, (1996) 
  12. Jun Li, Algebraic geometric interpretation of Donaldson’s polynomial invariants, J. Differential Geom. 37 (1993), 417-466 Zbl0809.14006MR1205451
  13. Alina Marian, Dragos Oprea, A tour of theta dualities on moduli spaces of sheaves, Curves and abelian varieties 465 (2008), 175-201, Amer. Math. Soc., Providence, RI Zbl1149.14301MR2457738
  14. Alina Marian, Dragos Oprea, Generic strange duality for K 3 surfaces, Duke Math. J. 162 (2013), 1463-1501 Zbl1275.14037MR3079253
  15. I. I. Piatetski-Shapiro, I. R. Shafarevich, A Torelli theorem for algebraic surfaces of type K 3 , Math. USSR Izvestia 5 (1971), 547-588 Zbl0253.14006
  16. Justin Sawon, Abelian fibred holomorphic symplectic manifolds, Turkish J. Math. 27 (2003), 197-230 Zbl1065.53067MR1975339
  17. Luca Scala, Dualité étrange de Le Potier et cohomologie du schéma de Hilbert ponctuel d’une surface, Gaz. Math. (2007), 53-65 Zbl1120.14032MR2319915
  18. Luca Scala, Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles, Duke Math. J. 150 (2009), 211-267 Zbl1211.14012MR2569613

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.