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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 齊震宇 | |
| dc.contributor.author | Yung-Yu Lei | en |
| dc.contributor.author | 雷永裕 | zh_TW |
| dc.date.accessioned | 2021-06-15T13:53:38Z | - |
| dc.date.available | 2016-09-13 | |
| dc.date.copyright | 2016-09-13 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-02-19 | |
| dc.identifier.citation | [1] A. Altman and S.L. Kleiman. Introduction to Grothendieck duality theory. Lecture notes in mathematics. Springer-Verlag, 1970.
[2] O. Debarre. Higher-Dimensional Algebraic Geometry. Hochschultext / Universitext. Springer, 2001. [3] B. Fantechi. Fundamental Algebraic Geometry: Grothendieck’s FGA Explained. Mathematical surveys and monographs. American Mathematical Society, 2005. [4] L. Fu. Algebraic Geometry. Mathematics series for graduate students. Tsinghua University Press, 2006. [5] A. Grothendieck. Elements de geometrie algebrique. I: Le langage des schemas. Publ. Math., Inst. Hautes Etud. Sci., 4:1–228, 1960. [6] A. Grothendieck. Elements de geometrie algebrique. II: Etude globale elementaire de quelques classe de morphismes. Publ. Math., Inst. Hautes Etud. Sci., 4:1–228, 1961. [7] A. Grothendieck. Techniques de construction et theoremes d’existence en geometrie algebrique. IV: Les schemas de Hilbert. Sem. Bourbaki 13(1960/61), No.221, 28 p. (1961)., 1961. [8] A. Grothendieck. Elements de geometrie algebrique. IV: Etude locale des schemas et des morphismes de schemas. (Troisieme partie). Redige avec la colloboration de Jean Dieudonne. Publ. Math., Inst. Hautes Etud. Sci., 28:1–255, 1966. [9] C.D. Hacon and S. Kovacs. Classification of Higher Dimensional Algebraic Varieties. Oberwolfach Seminars. Birkhauser Basel, 2011. [10] R. Hartshorne. Algebraic Geometry. Encyclopaedia of mathematical sciences. Springer, 1977. [11] J. Kollar. Rational Curves on Algebraic Varieties. A Series of Modern Surveys in Mathematics Series. Springer, 1996. [12] H. Matsumura. Commutative Algebra. Math Lecture Notes Series. Benjamin/Cummings Publishing Company, 1980. [13] H. Matsumura and M. Reid. Commutative Ring Theory. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1989. [14] Shigefumi Mori. Projective manifolds with ample tangent bundles. Annals of Mathematics, 1979. [15] D. Mumford. Abelian Varieties. Oxford University Press. [16] D. Mumford. Lectures on Curves on an Algebraic Surface. Annals of mathematics studies. Princeton University Press, 1966. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/51856 | - |
| dc.description.abstract | 本文分成兩個部分。第一個部分介紹希爾伯特概形與Hom概形的建構及建構所需的預備定理。第二部分探討一些Hom概形的局部結構：切空間的結構與維度估計，並運用這些結果來證明Mori的扳斷引理及一個有關Fano簇上的有理曲線之存在性定理。 | zh_TW |
| dc.description.abstract | There are two parts in this thesis. The first part consists of constructions of Hilbert schemes and Hom schemes with their preliminaries. The second part is some local properties of Hom schemes, structure of its tangent spaces and estimation of its dimension, and their applications: proving Mori's bend-and-break lemmas and a theorem about the existence of rational curves on Fano varieties. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T13:53:38Z (GMT). No. of bitstreams: 1 ntu-104-R01221029-1.pdf: 431824 bytes, checksum: 2b6287c7b30ba8ec0c25438000482301 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 致謝 i
中文摘要 ii Abstract iii Contents iv 1 Introduction 1 2 Preliminaries 3 2.1 Mumford-Castelnuovo Regularity . . . . . . . . . . . . . . . . . . . . . 3 2.2 Flattening Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Construction of Grassmannian 13 3.1 The Grassmannian Functor . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Construction of Grassmannian . . . . . . . . . . . . . . . . . . . . . . . 14 4 Construction of Hilbert Schemes 16 4.1 The Hilbert Functor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2 Construction of Hilbert Schemes . . . . . . . . . . . . . . . . . . . . . . 17 4.3 The Hom Functor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.4 Construction of Hom Schemes . . . . . . . . . . . . . . . . . . . . . . . 22 5 Local Properties of the Hom Scheme 26 5.1 Local Structure of Hom (X, Y ) . . . . . . . . . . . . . . . . . . . . . . 26 5.2 Dimension Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 A Slightly More General Situation and a Special Situation . . . . . . . . 31 6 The Bend and Break 32 6.1 The Bend and Break . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7 Rational Curves on Fano Varieties 37 7.1 Rational Curves on Fano Varieties . . . . . . . . . . . . . . . . . . . . . 37 Bibliography 40 | |
| dc.language.iso | en | |
| dc.subject | 扳斷引理 | zh_TW |
| dc.subject | 希爾伯特概形 | zh_TW |
| dc.subject | Hom概形 | zh_TW |
| dc.subject | Bend and break | en |
| dc.subject | Hilbert scheme | en |
| dc.subject | Hom scheme | en |
| dc.title | 希爾伯特概形之建構及其局部性質與應用 | zh_TW |
| dc.title | Construction of Hilbert Schemes with its Local Properties and Applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林惠雯,莊武諺 | |
| dc.subject.keyword | 希爾伯特概形,Hom概形,扳斷引理, | zh_TW |
| dc.subject.keyword | Hilbert scheme,Hom scheme,Bend and break, | en |
| dc.relation.page | 40 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2015-02-23 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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