Study of vector bundles using the theory of complexes

• Project/Area Number: 22340010
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kobe University
• Principal Investigator: YOSHIOKA Kota 神戸大学, 理学(系)研究科(研究院), 教授 (40274047)
• Co-Investigator(Renkei-kenkyūsha): NOUMI Masatoshi (80164672) ; YAMADA Yasuhiko (00202383) ; SAITO Masahiko (80183044) ; NAKAJIMA Hiraku (00201666) ; ABE Takeshi (90362409)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥11,570,000 (Direct Cost: ¥8,900,000、Indirect Cost: ¥2,670,000); Fiscal Year 2013: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2012: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2011: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2010: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
• Keywords: ベクトル束 / Bridgeland stability / モジュライ / 導来圏 / 複体

Research Abstract

I studied moduli of Bridgeland stable objects on an abelian or a K3 surface.
In particular, I proved that moduli spaces are projective varieties, and studied birational properties of the spaces. I also apply these results to the classification of vector bundles on abelian surfaces. I also proved the Witten conjecture of Donaldson invariants for algebraic surfaces.

Research Products

• [Journal Article] Some moduli spaces of Bridgeland's stability conditions (2015)
  • Author(s): Minamide Hiroki., Yanagida Shintarou, Yoshioka Kota
  • Journal Title: International Mathematics Research Notices, rnt126 Volume: 未定 Issue: 19 Pages: 64-64
  • DOI: 10.1093/imrn/rnt126
  • Peer Reviewed
• [Journal Article] Bridgeland's stabilities on abelian surfaces (2014)
  • Author(s): Yanagida Shintarou, Yoshioka Kota
  • Journal Title: Math. Z Volume: 276(arXiv:1203.0884) Issue: 1-2 Pages: 571-610
  • DOI: 10.1007/s00209-013-1214-1
  • Peer Reviewed
• [Journal Article] Semi-homogeneous sheaves, Fourier-Mukai transforms and moduli of stable sheaves on abelian surfaces (2013)
  • Author(s): S.Yanagida, K.Yoshioka
  • Journal Title: Journal fur die reine und angewandte Mathematik Volume: (印刷中)(掲載確定) Issue: 684 Pages: 31-86
  • DOI: 10.1515/crelle-2011-0010
  • Peer Reviewed
• [Journal Article] Perverse coherent sheaves and Fourier - Mukai transforms on surfaces (2013)
  • Author(s): Yoshioka, Kota
  • Journal Title: I. Kyoto J. Math Volume: 53(2) Issue: 2 Pages: 261-344
  • DOI: 10.1215/21562261-2081234
  • Peer Reviewed
• [Journal Article] Moduli of unramified irregular singular parabolic connections on a smooth projective curve (2013)
  • Author(s): Inaba Michiaki, Saito Masa-Hiko
  • Journal Title: Kyoto J. Math Volume: 53(2) Issue: 2 Pages: 433-482
  • DOI: 10.1215/21562261-2081261
  • Peer Reviewed
• [Journal Article] Perverse coherent sheaves and Fourier-Mukai transforms on surfaces, I (2013)
  • Author(s): Yoshioka Kota
  • Journal Title: Kyoto Journal of Mathematics Volume: 53
  • Peer Reviewed
• [Journal Article] Localization with a surface operator, irregular conformal blocks and open topological string (2012)
  • Author(s): Awata Hidetoshi, Fuji Hiroyuki, Kanno Hiroaki, Manabe Masahide, Yamada Yasuhiko
  • Journal Title: Adv. Theor. Math. Phys Volume: 16(3) Pages: 725-804
  • Peer Reviewed
• [Journal Article] Perverse coherent sheaves on blow-up III : Blow-up formula from wall-crossing (2011)
  • Author(s): H.Nakajima, K.Yoshioka
  • Journal Title: Kyoto Journal of Mathematics Volume: 51 Issue: 2 Pages: 263-335
  • DOI: 10.1215/21562261-1214366
  • Peer Reviewed
• [Journal Article] Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting (2011)
  • Author(s): Goettsche Lothar, Nakajima Hiraku, Yoshioka Kota
  • Journal Title: Publ. Res. Inst. Math. Sci Volume: 47(1) Pages: 307-359
  • NAID: 110008425903
  • Peer Reviewed
• [Journal Article] Birational maps of moduli spaces of vector bundles on K3 surfaces (2011)
  • Author(s): Kimura, Masanori, Yoshioka, Kota
  • Journal Title: Tokyo J. Math Volume: 34(2) Pages: 473-491
  • Peer Reviewed
• [Journal Article] Perverse coherent sheaves on blow-up I : a quiver description (2011)
  • Author(s): Nakajima H., Yoshioka K.
  • Journal Title: Advanced Studies in Pure Math Volume: 61 Pages: 349-386
  • Peer Reviewed
• [Journal Article] Perverse coherent sheaves on blow-up II : Wall-crossing and Betti numbers formula (2011)
  • Author(s): Nakajima H., Yoshioka K.
  • Journal Title: J.Algebraic Geometry Volume: 29 Pages: 47-100
  • NAID: 120005593584
  • Peer Reviewed
• [Journal Article] Perverse coherent sheaves and Fourier-Mukai transforms on surfaces
  • Author(s): Yoshioka Kota
  • Journal Title: Kyoto J. Math Volume: (出版予定)
  • Peer Reviewed
• [Journal Article] Perverse coherent sheaves on blow-up III : Blow-up formula from wall-crossing
  • Author(s): Nakajima H., Yoshioka K
  • Journal Title: Kyoto Journal of Mathematics Volume: (掲載確定)
  • NAID: 120005593586
  • Peer Reviewed
• [Journal Article] Donaldson=Seiberg-Witten from Mochizuki's formula and instanton counting
  • Author(s): Goettsche L., Nakajima H., Yoshioka K.
  • Journal Title: Publ.Res.Inst.Math.Sci. Volume: (掲載確定)
  • NAID: 110008425903
  • Peer Reviewed
• [Presentation] Bridgeland stability and stable sheaves on abelian surfaces (2013)
  • Author(s): 吉岡康太
  • Organizer: The 6th MSJ-SI --Development of Moduli Theory
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Bridgeland stability and stable sheaves on abelian surfaces (2013)
  • Author(s): Kota Yoshioka
  • Organizer: The 6th MSJ-SI -- Development of Moduli Theory
  • Place of Presentation: RIMS
• [Presentation] Bridgeland stability conditions and Fourier-Mukai transforms (2011)
  • Author(s): 吉岡康太
  • Organizer: Moduli spaces closing conference
  • Place of Presentation: Newton Institute 英国
• [Presentation] Bridgeland stability conditions and Fourier-Mukai transforms (2011)
  • Author(s): 吉岡康太
  • Organizer: Moduli spaces closing conference
  • Place of Presentation: Newton Institute
• [Presentation] 代数曲面のDonaldson不変量について (2010)
  • Author(s): 吉岡康太
  • Organizer: 幾何学シンポジウム
  • Place of Presentation: 神戸大学理学研究科
  • Year and Date: 2010-08-07
• [Presentation] 代数曲面のDonaldson不変量について (2010)
  • Author(s): 吉岡康太
  • Organizer: 幾何学シンポジウム
  • Place of Presentation: 神戸大学理学研究科(兵庫県)(招待講演)
  • Year and Date: 2010-08-07
• [Presentation] Instanton counting and Donaldson invariants (2010)
  • Author(s): 中島啓
  • Organizer: Hardy Lectures
  • Place of Presentation: London
  • Year and Date: 2010-07-02