Fourier–Mukai partners of elliptic ruled surfaces
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Abstract:
We study Fourier–Mukai partners of elliptic ruled surfaces. We also describe the autoequivalence group of the derived categories of ruled surfaces with an elliptic fibration, by using another work of the author.References
- A.I. Bondal and D.O. Orlov, Semiorthogonal decomposition for algebraic varieties, alg-geom 9712029.
- Wolf P. Barth, Klaus Hulek, Chris A. M. Peters, and Antonius Van de Ven, Compact complex surfaces, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 4, Springer-Verlag, Berlin, 2004. MR 2030225, DOI 10.1007/978-3-642-57739-0
- Tom Bridgeland, Fourier-Mukai transforms for elliptic surfaces, J. Reine Angew. Math. 498 (1998), 115–133. MR 1629929, DOI 10.1515/crll.1998.046
- Tom Bridgeland and Antony Maciocia, Complex surfaces with equivalent derived categories, Math. Z. 236 (2001), no. 4, 677–697. MR 1827500, DOI 10.1007/PL00004847
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Toshiyuki Katsura and Kenji Ueno, On elliptic surfaces in characteristic $p$, Math. Ann. 272 (1985), no. 3, 291–330. MR 799664, DOI 10.1007/BF01455561
- Yujiro Kawamata, $D$-equivalence and $K$-equivalence, J. Differential Geom. 61 (2002), no. 1, 147–171. MR 1949787
- Masaki Maruyama, On automorphism groups of ruled surfaces, J. Math. Kyoto Univ. 11 (1971), 89–112. MR 280493, DOI 10.1215/kjm/1250523688
- D. O. Orlov, Equivalences of derived categories and $K3$ surfaces, J. Math. Sci. (New York) 84 (1997), no. 5, 1361–1381. Algebraic geometry, 7. MR 1465519, DOI 10.1007/BF02399195
- T. Togashi, Daen fibration wo motsu seihyousuu no sensiki kyokumen ni tsuite (in Japanese), Master’s Thesis, Tokyo Metropolitan University, (2011).
- Hokuto Uehara, An example of Fourier-Mukai partners of minimal elliptic surfaces, Math. Res. Lett. 11 (2004), no. 2-3, 371–375. MR 2067481, DOI 10.4310/MRL.2004.v11.n3.a9
- Hokuto Uehara, A counterexample of the birational Torelli problem via Fourier-Mukai transforms, J. Algebraic Geom. 21 (2012), no. 1, 77–96. MR 2846680, DOI 10.1090/S1056-3911-2011-00551-1
- H. Uehara, Autoequivalences of derived categories of elliptic surfaces with non-zero Kodaira dimension, Algebraic Geometry 2 (5) (2016), 543-577, DOI 10.14231/AG-2016-025
- H. Uehara, A trichotomy for the autoequivalence groups on smooth projective surfaces (in preparation).
Additional Information
- Hokuto Uehara
- Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minamiohsawa, Hachioji-shi, Tokyo, 192-0397, Japan
- MR Author ID: 663390
- Email: hokuto@tmu.ac.jp
- Received by editor(s): March 10, 2016
- Received by editor(s) in revised form: August 29, 2016
- Published electronically: February 10, 2017
- Additional Notes: The author was supported by the Grants-in-Aid for Scientific Research (No.23340011).
- Communicated by: Lev Borisov
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3221-3232
- MSC (2010): Primary 14J27, 14F05, 18E30
- DOI: https://doi.org/10.1090/proc/13471
- MathSciNet review: 3652778