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Deformations of curves on a higher dimensionalalgebraic variety and their obstructions

Research Project

Project/Area Number 23740032
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionTokai University

Principal Investigator

NASU Hirokazu  東海大学, 理学部, 講師 (30535331)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsヒルベルトスキーム / 変形理論 / 空間曲線 / 無限小変形 / 障害 / 障害類 / デルペッツォ多様体
Research Abstract

We study the first order infinitesimal deformations of degenerate curves on a uniruled algebraic variety of dimension at least 3 and their obstructions. As a result, we give two different geometric interpretations of infinitesimal deformations with poles (rational sections of the normal bundle of hypersurfaces). By using the liaison theory, we give a classification of the irreducible components of the Hilbert scheme for a certain class of space curves. We also study the deformations of space curves lying on a smooth quartic surface of Picard number 2, and construct a new example of families of curves with obstructed first order infinitesimal deformations.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Research-status Report
  • Research Products

    (14 results)

All 2013 2012 2011 Other

All Presentation (12 results) (of which Invited: 1 results) Remarks (2 results)

  • [Presentation] Obstructions to deforming space curves and non-reduced components of the Hilbert scheme2013

    • Author(s)
      Hirokazu Nasu
    • Organizer
      Algebra-Seminaret i Oslofjord-Regionen
    • Place of Presentation
      Oslo and Akershus University College (ノルウェー)
    • Year and Date
      2013-03-05
    • Related Report
      2012 Final Research Report
  • [Presentation] Obstructions to deforming space curves and non-reduced components of the Hilbert scheme2012

    • Author(s)
      那須弘和
    • Organizer
      Workshop in Hawaii: Aspects of SLP and WLP
    • Place of Presentation
      Hawaii Tokai International College (米国)
    • Year and Date
      2012-09-14
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] 3次元単線織多様体上の曲線の変形障害について2012

    • Author(s)
      那須弘和
    • Organizer
      第10回アフィン代数幾何学研究集会
    • Place of Presentation
      関西学院大学大阪梅田キャンパス
    • Year and Date
      2012-09-06
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] 3次元単線織多様体上の曲線の変形障害について2012

    • Author(s)
      那須弘和
    • Organizer
      東京理科大学談話会
    • Place of Presentation
      東京理科大学理工学部数学科
    • Year and Date
      2012-07-20
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] 空間曲線のリエゾンとヒルベルトスキームの既約成分2012

    • Author(s)
      那須弘和
    • Organizer
      研究集会「可換環論と鏡映群の表現論」
    • Place of Presentation
      東海大学理学部
    • Year and Date
      2012-03-08
    • Related Report
      2012 Final Research Report
  • [Presentation] 3次元単線織多様体上の曲線の変形障害について2012

    • Author(s)
      那須弘和
    • Organizer
      代数学セミナー
    • Place of Presentation
      広島大学理学部数学科
    • Year and Date
      2012-02-03
    • Related Report
      2012 Final Research Report
  • [Presentation] 3次元単線織多様体上の曲線の変形障害について2012

    • Author(s)
      那須弘和
    • Organizer
      代数学セミナー(招待講演)
    • Place of Presentation
      広島大学理学部数学科
    • Related Report
      2011 Research-status Report
  • [Presentation] 空間曲線のリエゾンとヒルベルトスキームの既約成分2012

    • Author(s)
      那須弘和
    • Organizer
      研究集会「可換環論と鏡映群の表現論」(招待講演)
    • Place of Presentation
      東海大学理学部
    • Related Report
      2011 Research-status Report
  • [Presentation] Obstructions to deforming curves on a uniruled 3-fold2011

    • Author(s)
      那須弘和
    • Organizer
      代数幾何学セミナー
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2011-12-05
    • Related Report
      2012 Final Research Report
  • [Presentation] Obstructions to deforming degenerate curves on a scroll2011

    • Author(s)
      那須弘和
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      信州大学理学部
    • Year and Date
      2011-09-30
    • Related Report
      2012 Final Research Report 2011 Research-status Report
  • [Presentation] Obstructions to deforming curves on a uniruled 3-fold2011

    • Author(s)
      那須弘和
    • Organizer
      代数幾何学セミナー(招待講演)
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2011 Research-status Report
  • [Presentation] Obstructions to deforming space curves and non-reduced components of the Hilbert scheme

    • Author(s)
      那須弘和
    • Organizer
      Algebra-Seminaret i Oslofjord-Regionen
    • Place of Presentation
      Oslo and Akershus University College (ノルウェー)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Remarks]

    • URL

      http://fuji.ss.u-tokai.ac.jp/nasu/

    • Related Report
      2012 Final Research Report
  • [Remarks] 研究者webページ

    • URL

      http://fuji.ss.u-tokai.ac.jp/nasu/index.html

    • Related Report
      2012 Annual Research Report

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Published: 2011-08-05   Modified: 2019-07-29  

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