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1997 Fiscal Year Final Research Report Summary

Study of moduli spaces -compactification and period map

Research Project

Project/Area Number 08454004
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

SAITO Hiroshi  Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (80135293)

Co-Investigator(Kenkyū-buntansha) TERANISHI Yasuo  Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (20115603)
TANIGAWA Yoshio  Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (50109261)
FUJIWARA Kazuhiro  Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (00229064)
NAMIKAWA Yukihiko  Nagoya University, Graduate School of Polymathematics, Professor, 大学院多元数理科学研究科, 教授 (20022676)
NAITO Hisashi  Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (40211411)
Project Period (FY) 1996 – 1997
Keywordsmoduli space / geometric invariant theory / louuded syumelric domain / period map / abelian surface / thete function / Horroch-Mumford
Research Abstract

1. We held a workshop on the moduli space in May as sheduled in Nagoya
University invitiing Profeeeors Alexeev and Sankaran. We discussed the canonical compactification of the moduli space of principally polarized abelian varieties constructed by Nakamura and Alexeev. In this study, we have constructed natural birational map between the moduli space of polarized abelian surfaces of degree 8 (resp.10) and the octahedral (resp.icosahedral) 3-fold. We found that the notion of log variety makes the construction clearer and that a complete integral system is related in the case of degree 8.
2. We defined a new quotient of algerbaic variety by an action of an algebraic group which is independent of the choice of a linearization. We are now examining this new quotient in examples.
3. Comparing the moduli space M of cubic 4-folds obtained from the geometric invariant theory with the period domain, we found a candidate for good geometric compactification M.This compactification suggests a good compactification of the moduli for K3 surfaces also.

  • Research Products

    (17 results)

All Other

All Publications (17 results)

  • [Publications] MUKAI, Shigeru: "Curves and K3 surfaces of genus eleven" Module of recfor bundles (ed Marugama). 189-197 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 向井 茂: "単純Lie環とLegendre多様体" 名古屋数理フォーラム. 3. 1-12 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 向井 茂: "Brill-Noeriler理論の非可控化と3次元Fano多様体" 数学. 49. 1-24 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] MUKAI, Shigeru: "Lattce theoretic construction of symplectic actions on K3 surfaces" Duke Marh J.to oppear.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] REID, Miles: "Chapters on algebraic surfaces" IAS/Park City Leeof Nok Siries. 1-154 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] FUJIWARA, Kazuhiro: "Riged germetry Lefschely-Verdrer frace formala and Delegnic conjecfare" Jnvent and Mark. 127. 489-533 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 向井 茂: "「現代数学の展開」モジュライ理論1,2" 岩波書店, 約200 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] REID, Miles: "Algebraic Geometry Enroconference" Cambridge大学出版, 約400 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] MAUKI,shigeru: "Curves and K3 surfaces of genus eleven. Moduli of Vector Bundles (Maruyama M.ed.)" Pure and Applied Math.189-197 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mukai, Shigeru: "Simple Lie albebra and Legebdre variety" Nagoya Suri Forum. Vol.3. 1-12

    • Description
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  • [Publications] Mukai, Shigeru: "Non abelian Brill Noether theory" Sugaku. Vol.49.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] MUKAI,Shigeru: "Lattice theoretic construction of symlectic action on K3 surfaces" Duke Math.J. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] MUKAI,Shigeru: "Duality of polarized K3 surfaces. Proceedings of Euroconference on Algebraic Geometry" London Math, Soc.Lect. Note series.

    • Description
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  • [Publications] REID,Miles: "Chapters on algebraic surfaces Complex algebraic varieties, J.Kollar (eds)" Park City Lect. Note Series. 1-154. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] FUJIKAWA,Kazuhiro: "Rigid geometry, Lefschetz-Verdier trace formula, and Deligne's conjecture." Inv.Math.127. 489-533 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] REID,Miles: Algebraic geometry EuroConference (Warwick, Jul 1996). Cambridge Univ.Press,

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  • [Publications] REID,Miles: 3-folds at Warwick. Cambridge Univ.Press,

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      「研究成果報告書概要(欧文)」より

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Published: 1999-03-16  

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