On a certain generalization of spherical twists

Yukinobu Toda

Bulletin de la Société Mathématique de France (2007)

  • Volume: 135, Issue: 1, page 119-134
  • ISSN: 0037-9484

Abstract

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This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of ( 0 , - 2 ) -curves on threefolds, or deforming ℙ -objects introduced by D.Huybrechts and R.Thomas.

How to cite

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Toda, Yukinobu. "On a certain generalization of spherical twists." Bulletin de la Société Mathématique de France 135.1 (2007): 119-134. <http://eudml.org/doc/272512>.

@article{Toda2007,
abstract = {This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of $(0, -2)$-curves on threefolds, or deforming $\mathbb \{P\}$-objects introduced by D.Huybrechts and R.Thomas.},
author = {Toda, Yukinobu},
journal = {Bulletin de la Société Mathématique de France},
keywords = {derived categories; mirror symmetries},
language = {eng},
number = {1},
pages = {119-134},
publisher = {Société mathématique de France},
title = {On a certain generalization of spherical twists},
url = {http://eudml.org/doc/272512},
volume = {135},
year = {2007},
}

TY - JOUR
AU - Toda, Yukinobu
TI - On a certain generalization of spherical twists
JO - Bulletin de la Société Mathématique de France
PY - 2007
PB - Société mathématique de France
VL - 135
IS - 1
SP - 119
EP - 134
AB - This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of $(0, -2)$-curves on threefolds, or deforming $\mathbb {P}$-objects introduced by D.Huybrechts and R.Thomas.
LA - eng
KW - derived categories; mirror symmetries
UR - http://eudml.org/doc/272512
ER -

References

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  1. [1] A. Bondal & D. Orlov – « Semiorthogonal decomposition for algebraic varieties », preprint, 1995, arXiv:math.AG/9506012, p. 1–55. 
  2. [2] T. Bridgeland – « Equivalences of triangulated categories and Fourier-Mukai transforms », Bull. London Math. Soc.31 (1999), p. 25–34. Zbl0937.18012MR1651025
  3. [3] —, « Flops and derived categories », Invent. Math.147 (2002), p. 613–632. Zbl1085.14017MR1893007
  4. [4] J.-C. Chen – « Flops and equivalences of derived categories for three-folds with only Gorenstein singularities », J. Differential Geom.61 (2002), p. 227–261. Zbl1090.14003MR1972146
  5. [5] D. Huybrechts & R. Thomas – « ℙ -objects and autoequivalences of derived categories », preprint, 2005, arXiv:math.AG/0507040, p. 1–13. Zbl1094.14012MR2200048
  6. [6] M. Inaba – « Toward a definition of moduli of complexes of coherent sheaves on a projective scheme », J. Math. Kyoto Univ. 42-2 (2002), p. 317–329. Zbl1063.14013MR1966840
  7. [7] A. Ishii & H. Uehara – « Autoequivalences of derived categories on the minimal resolutions of A n -singularities on surfaces », preprint, 2004, arXiv:math.AG/0409151, p. 1–53. Zbl1097.14013
  8. [8] M. Kontsevich – « Homological algebra of mirror symmetry », in Proceedings of the International Congress of Mathematicians, Zurich (1994) vol. I, Birkhäuser, 1995, p. 120–139. Zbl0846.53021MR1403918
  9. [9] M. Lieblich – « Moduli of complexes on a proper morphism », J. Algebraic Geom.15 (2006), p. 175–206. Zbl1085.14015MR2177199
  10. [10] D. Ploog – « Autoequivalences of derived categories of smooth projective varieties », Thèse, 2005. 
  11. [11] P. Seidel – « Graded Lagrangian submanifolds », Bull. Soc. Math. France128 (2000), p. 103–149. Zbl0992.53059MR1765826
  12. [12] P. Seidel & R. Thomas – « Braid group actions on derived categories of coherent sheaves », Duke Math. J.108 (2001), p. 37–107. Zbl1092.14025MR1831820
  13. [13] R. Thomas – « A holomorphic casson invariant for Calabi-Yau 3-folds and bundles on K 3 -fibrations », J. Differential Geom.54 (2000), p. 367–438. Zbl1034.14015MR1818182
  14. [14] Y. Toda – « Stability conditions and crepant small resolutions », preprint, 2005, arXiv:math.AG/0512648, p. 1–25. Zbl1225.14030MR2425708

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