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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱 | |
| dc.contributor.author | Hsin-Ku Chen | en |
| dc.contributor.author | 陳星谷 | zh_TW |
| dc.date.accessioned | 2021-06-16T23:57:29Z | - |
| dc.date.available | 2012-08-15 | |
| dc.date.copyright | 2012-08-15 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-17 | |
| dc.identifier.citation | [B] A.Beaville, Complex Algebraic Surfaces, Astérisque, no. 54, 1978.
[B2] A. Beauville, L'inégalité pg ≥ 2q−4 pour les surfaces de type général, Bull. Soc. math. France, 110, 1982, p.343-346. [BCG] I. Bauer, F. Catanese, F. Grunewald, The classification of surfaces with pg = q = 0 isogenous to a product of curves, e-print math.AG/0610267 (2006) (2002), no.7, 2631-2638. [BL] C. Birkenhake, H. Lange, Complex Abelian Varieties, Grundlehreb der mathematischen Wissenschaften 302, Springer-Verlag Berlin Heidelberg 1992. [C] F. Catanese, Fibred surfaces, varieties isogenous to a product and related moduli spaces, Amer. J. Math. 122, (2000), 1-44. [CH] J. A. Chen and C. D. Hacon, An example of a surface of general type with pg = q = 2 and K2 X = 5 Pacific. J. Math. 223 no. 2, (2006), 219-228. [CP] G. Carnovale, F. Polizzi, The classification of surfaces of general type with pg = q = 1 isogenous to a product, e-print arXiv: 0704.0446, 2007, Adv. Geom., in press. [D] O. Debarre, Inégalités numériques pour les surfaces de type général, Bull. Soc.Math. de France, vol. 110 (1982), 319-346. [HM] D. W. Hahn, R. Miranda, Quadruple covers of algebraic varieties, J. Algebraic Geom., 8 (1999), 1-30. [HP] C. D. Hacon and R. Pardini, Surfaces with pg = q = 3, Trans. Amer. Math. Soc.354 [M] R. Miranda, Triple covers in algebraic geometry. Amer. J. Math. 107, no. 5, 1123-1158 [Mo] S. Mori, Classification of higher-dimensional varieties, Algebraic geometry,Proc. Symp. Pure Math. 46, Part 1 Amer. Math. Soc. (1987) pp. 165-171. [Mu] S. Mukai, Duality between D(X) and D( ˆX ) with its application to Picard sheaves, Nagoya Math. Juor 81,(1981) 153-175. [S] T. Szamuely, Galois groups and fundamental groups, Cambridge studies in advanced mathematics, vol. 117, Cambridge University Press, 2009. [P] M. Penegini, The classification of isotrivially fibred surfaces with pg = q = 2,arXiv: 0904.1352. [Y] S. T. Yau, Calabis conjecture and some new results in algebraic geometry, Proc.Nat. Acad. Sci. USA 74 (1977), 1798-1799 [Z] F. Zucconi, Surfaces with pg = q = 2 and an irrational pencil, Canad. J. Math.Vol. 55, (2003), 649-672.26 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65668 | - |
| dc.description.abstract | 這篇文章主要是在探討代數曲面的分類理論。特別地我們考慮虧格數與非正則數均為二的一般形曲面，到目前為止，對於這一種曲面的分類還是不完全的。我所做的事是在於真正構造出實際的例子。在這篇文章中我們考慮兩種構造曲面的方法。第一種做法是考慮與兩條曲線乘積同源的曲面。這一類的曲面有一些好的性質，所以在討論上是相對容易的。佩納吉尼做出了一張列表，把這類的曲面完全分類完畢了。第二種做法是去考慮在阿貝爾的曲面上的有限覆蓋。陳榮凱與黑肯利用阿貝爾曲面上的三次覆蓋造出了一個例子。我依循他們的做法，利用阿貝爾曲面上的四次覆蓋造出了另外一個這樣的曲面。 | zh_TW |
| dc.description.abstract | This article is about the classification of algebraic surfaces. We focus on the surfaces of general type with pg = q = 2. This kind of surfaces are not completely classified yet.We construct several examples in this article.In this paper I discuss two methods for constructing a surface of general type with pg = q = 2. The first one is by considering a surface which is isogenus to a product of curves. This kind of surfaces is rather easy to work out. Penegini gives a complete list of such surfaces. The other way to construct a surface with given invariant is to consider a finite covering of an abelain surface. Chen and Hacon construct a surface with K2 = 5
by considering a triple cover of an abelian surface. Using the similar method, I construct a quadruple covering over an abelian surface to get a surface with K2 = 6. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T23:57:29Z (GMT). No. of bitstreams: 1 ntu-101-R99221005-1.pdf: 318653 bytes, checksum: db54b4534fb2ee6f3bda8124972f67e7 (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 口試委員審定書i
誌謝ii 中文摘要iii 英文摘要iv 1 Introduction 1 2 Techniques 2 2.1 Some facts about surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Quotient construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Covering construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Main theorems 12 3.1 Surfaces constructed by quotient construction . . . . . . . . . . . . . . . 12 3.2 Surfaces constructed by covering construction . . . . . . . . . . . . . . . 16 | |
| dc.language.iso | en | |
| dc.subject | 一般形曲面 | zh_TW |
| dc.subject | 曲線乘積同源 | zh_TW |
| dc.subject | 阿貝爾曲面 | zh_TW |
| dc.subject | isogenus to product | en |
| dc.subject | surface of general type | en |
| dc.subject | abelian surface | en |
| dc.title | 虧格數和非正則數均為二的一般形曲面的研究 | zh_TW |
| dc.title | Surfaces of general type with p_g=q=2 | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡炎龍,江謝宏任 | |
| dc.subject.keyword | 一般形曲面,曲線乘積同源,阿貝爾曲面, | zh_TW |
| dc.subject.keyword | surface of general type,isogenus to product,abelian surface, | en |
| dc.relation.page | 26 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-07-18 | |
| 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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