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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 莊武諺 | zh_TW |
| dc.contributor.advisor | Wu-Yen Chuang | en |
| dc.contributor.author | 王偉 | zh_TW |
| dc.contributor.author | Wei Wang | en |
| dc.date.accessioned | 2023-08-01T16:26:15Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-01 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-07-07 | - |
| dc.identifier.citation | [BPS80] Constantin Bănică, Mihai Putinar, and Georg Schumacher. Variation der globalen ext in deformationen kompakter komplexer räume. Math. Ann., 250(2):135–155, 1980.
[Bri12] Tom Bridgeland. An introduction to motivic hall algebras. Adv. in Math., 229(1):102–138, 2012. [Bru90] Rogier Brussee. Stable bundles on blown up surfaces. Math. Zeit., 205:551–565, 1990. [FQ95] Robert Friedman and Zhenbo Qin. Flips of moduli spaces and transition formulas for donaldson polynomial invariants of rational surfaces. Comm. in Anal. and Geom., 3(1):11–83, 1995. [Fri12] Robert Friedman. Algebraic surfaces and holomorphic vector bundles. Springer, 2012. [Gie77] David Gieseker. On the moduli of vector bundles on an algebraic surface. Ann. of Math., 106(1):45–60, 1977. [Göt96] Lothar Göttsche. Change of polarization and hodge numbers of moduli spaces of torsion free sheaves on surfaces. Math. Zeit., 223:247–260, 1996. [Gö00] Lothar Göttsche. On the motive of the hilbert scheme of points on a surface. Math. Res. Letr., 8, 08 2000. [GZLMH04] Sabir M Gusein-Zade, Ignacio Luengo, and Alejandro Melle-Hernàndez. A power structure over the grothendieck ring of varieties. Math. Res. Letr., 11(1):49–57, 2004. [Har13] Robin Hartshorne. Algebraic geometry, volume 52. Springer, 2013. [HL10] Daniel Huybrechts and Manfred Lehn. The geometry of moduli spaces of sheaves. Cambridge Univ. Prss., 2010. [Kos21] Naoki Koseki. Categorical blow-up formula for hilbert schemes of points. arXiv prepr. 2110.08315, 2021. [Lan83] Herbert Lange. Universal families of extensions. J. of Alg., 83(1):101–112, 1983. [LQ98] Wei-Ping Li and Zhenbo Qin. On blowup formulae for the s-duality conjecture of Vafa and Witten ii: The universal functions. Math. Res. Letr., 5, 06 1998. [LQ99] Wei-ping Li and Zhenbo Qin. On blowup formulae for the s-duality conjecture of Vafa and Witten. Invent. Math., 136(2):451–482, 4 1999. [Mac62] Ian G Macdonald. The poincaré polynomial of a symmetric product. In Math. Proc. of the Cambridge Phil. Soc., volume 58, pages 563–568. Cambridge Univ. Prss., 1962. [Mar75] Masaki Maruyama. Stable vector bundles on an algebraic surface. Nagoya Math. J., 58:25–68, 1975. [Mar77] Masaki Maruyama. Moduli of stable sheaves, i. J. of Math. of Kyoto Univ., 17(1):91–126, 1977. [Mar78] Masaki Maruyama. Moduli of stable sheaves, ii. J. of Math. of Kyoto Univ., 18(3):557–614, 1978. [Moz19] Sergey Mozgovoy. Motivic classes of quot-schemes on surfaces. arXiv prepr., 1911.07561, 2019. [Nak93] Tohru Nakashima. Moduli of stable bundles on blown up surfaces. J. of Math. of Kyoto Univ., 33(3):571–581, 1993. [NY03] Hiraku Nakajima and Kota Yoshioka. Lectures on instanton counting. Alg. Structs. and Moduli Spaces, 38, 12 2003. [Qin92] Zhenbo Qin. Moduli of stable sheaves on ruled surfaces and their picard groups. J. reine angew. Math., 426:201–219, 1992. [Qin93] Zhenbo Qin. Equivalence classes of polarizations and moduli spaces of sheaves. J. of Diff. Geo., 37(2):397–415, 1993. [Ric20] Andrea T Ricolfi. On the motive of the quot scheme of finite quotients of a locally free sheaf. J. Math. Pures Appl., 144:50–68, 2020. [Tod21] Yukinobu Toda. Derived categories of quot schemes of locally free quotients via categorified hall products. arXiv prep. 2110.02469, 2021. [VW94] Cumrun Vafa and Edward Witten. A strong coupling test of s-duality. Nucl. Phys. B, 431(1-2):3–77, 1994. [Yos94] Kota Yoshioka. The betti numbers of the moduli space of stable sheaves of rank 2 on p2. J. reine angew. Math., 1994. [Yos96] Kōta Yoshioka. Chamber structure of polarizations and the moduli of stable sheaves on a ruled surface. Intl. J. Math., 7:411–431, 1996 | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88019 | - |
| dc.description.abstract | 本篇論文主要宗旨係在推廣[LQ98a,LQ98b]中所做出來的一個從Vafa與Witten從S-對偶猜想中預測出來的一個描述代數曲面上穩定秩二層的模空間的不變量在獨異變換之下的公式。
該兩篇論文所考慮的不變量為virtual霍奇多項式；我們想要將這些結果作到動機的版本。 在這篇論文中，我們驗證[LQ99,LQ98]當中的一些證明可以推廣到動機的設定之下，並在這樣的框架之下我們藉由[Moz19]中的一個Quot概型的動機生成函數公式回答了一個於[LQ98]中提出的帶有組合味道的猜想。我們也簡化了[LQ98]當中的一些計算。 | zh_TW |
| dc.description.abstract | The purpose of this thesis is to generalize a collection of results in [LQ99,LQ98] concerning change of invariants of moduli space of rank-2 stable sheaves over an algebraic surface under blowup, which is a set of formulas predicted by Vafa and Witten in the context of the S-duality conjecture.
In these two papers, the invariants the authors considered are the virtual Hodge polynomials, and our goal is to refine these invariants to the settings of Grothendieck's motivic ring of varieties. In this paper, we verified that some of the proofs given in [LQ99,LQ98] can be generalized to the motivic setting, and by working in the motivic ring of varieties, we are able to answer a conjectural combinatorial formula posed in [LQ98], by using a formulae concerning motivic generating series of Quot schemes given in [Moz19]. We also simplified some of the calculations in [LQ98]. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-01T16:26:15Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-01T16:26:15Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix Chapter 1 Introduction 1 1.1 Overview 1 1.2 Organization of Contents 2 1.3 Frameworks and Notations 3 1.4 Summary of Main Results 6 1.5 Outline of Proof 11 Chapter 2 The Motivic Ring of Varieties 13 2.1 Definition and Generalities 13 2.2 Power Structures and Motivic Exponentials 15 Chapter 3 Moduli Spaces of Sheaves over Algebraic Surfaces 19 3.1 Stability and Polarization 19 3.2 The Moduli Functor and the Moduli Space 21 3.3 Change of Polarization - Chambers and Walls 25 3.4 Blowing-up and Stability 29 3.5 Compactification and Comparison 32 Chapter 4 Existence and Computation of Universal Functions 39 4.1 Existence of Universal Functions 39 4.2 Computation of Universal Functions (I) by Specialization 47 4.3 Computation of Universal Functions (II) by Recursion 54 References 63 Chapter 5 Appendix. A Survey on Related Results 67 | - |
| dc.language.iso | en | - |
| dc.subject | 獨異變換 | zh_TW |
| dc.subject | 代數曲面 | zh_TW |
| dc.subject | S-對偶性猜想 | zh_TW |
| dc.subject | 動機 | zh_TW |
| dc.subject | 穩定層的模空間 | zh_TW |
| dc.subject | Monoidal Transformations | en |
| dc.subject | Algebraic Surfaces | en |
| dc.subject | Motives | en |
| dc.subject | Moduli space of Stable Sheaves | en |
| dc.subject | S-Duality Conjecture | en |
| dc.title | 一個描述獨異變換之下代數曲面上秩二的層的模空間動機變換公式 | zh_TW |
| dc.title | A Motivic Blowup Formula of Moduli Spaces of Rank 2 Sheaves on a Smooth Projective Algebraic Surface | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 卓士堯;陳俊成;林學庸 | zh_TW |
| dc.contributor.oralexamcommittee | Shin-Yao Jow;Jiun-Cheng Chen;Hsueh-Yung Lin | en |
| dc.subject.keyword | 代數曲面,獨異變換,穩定層的模空間,動機,S-對偶性猜想, | zh_TW |
| dc.subject.keyword | Algebraic Surfaces,Monoidal Transformations,Moduli space of Stable Sheaves,Motives,S-Duality Conjecture, | en |
| dc.relation.page | 69 | - |
| dc.identifier.doi | 10.6342/NTU202301040 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-07-11 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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