請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50683
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 王金龍(Chin-Lung Wang),林惠雯(Hui-Wen Lin) | |
dc.contributor.author | Tsung-Ju Lee | en |
dc.contributor.author | 李宗儒 | zh_TW |
dc.date.accessioned | 2021-06-15T12:52:28Z | - |
dc.date.available | 2016-07-26 | |
dc.date.copyright | 2016-07-26 | |
dc.date.issued | 2016 | |
dc.date.submitted | 2016-07-19 | |
dc.identifier.citation | 1. A. Adolphson. Hypergeometric functions and rings generated by monomials. Duke Mathematical Journal, 73(2):269–290, 1994.
2. D. Abramovich and K. Karu. Weak semistable reduction in characteristic 0. Inventiones Mathematicae, 139(2):241–273, 2000. 3. V. V. Batryev. Dual polyhedra and mirror symmetry for Calabi–Yau hypersur- faces in toric varieties. Journal of Algebraic Geometry, 3:493–545, 1994. 4. V. V. Batryev and L. Borisov. On Calabi-Yau complete intersections in toric varieties. In Higher-dimensional complex varieties (Trento, 1994), pages 39–65. de Gruyter, Berlin, 1996. 5. V. V. Batryev, I. Ciocan-Fontanine, B. Kim, and D. V. Straten. Mirror symmetry and toric degenerations of partial flag manifolds. Acta Mathematica, 184(1):1– 39, 2000. 6. S. Bloch, A. Huang, B. Lian, V. Srinivas, and S.-T. Yau. On the holonomic rank problem. Journal of Differential Geometry, 97(11-35), 2014. 7. R. Bott. Homogeneous vector bundles. The Annals of Mathematics, 66(2):203– 248, 1957. 8. P. Candelas, X.dela Ossa, A. Font, S. Katz,and D. R. Morrison.Mirrorsymmetry for two-parameter models (i). Nuclear Physics B, 416:481–538, March 1994. 9. P. Candelas, P. Green, and Tristan Hubsch. Rolling among Calabi-Yau vacua. Nuclear Physics B, 330(1):49–102, 1990. 10. E. Cattani and A. Kaplan. Polarized mixed Hodge structures and the lo- cal monodromy of a variation of Hodge structure. Inventiones Mathematicae, 67:101–115, 1982. 11. E. Cattani, A. Kaplan, and W. Schmid. Degeneration of Hodge Structures. An- nals of Mathematics, 123:457–535, 1986. 12. David A. Cox. The homogeneous coordinate ring of a toric variety. Journal of Algebraic Geometry, 4(1):17–50, 1995. 13. David A. Cox. Erratum to “the homogeneous coordinate ring of a toric vari- ety”. Journal of Algebraic Geometry, 23(2):393–398, 2014. 14. S.-Y. Cheng and S.-T. Yau. On the existence of a complete Kahler metric on non-compact complex manifolds and regularity of Fefferman’s equation. Com- munications on Pure and Applied Mathematics, 33(4):507–544, 1980. 15. P. Deligne. Equations differentielles a points singuliers reguliers, volume 163 of Lecture Notes in Mathematics. Springer-Verlag, 1970. 16. S. Donaldson and S. Sun. Gromov–Hausdorff limits of Kahler manifolds and algebraic geometry. Acta Mathematica, 213(1):66–106, 2014. 17. R. Friedman. On threefolds with trivial canonical bundle. In Complex geometry and Lie theory, Proceedings of Symposia in Pure Mathematics, pages 103–134. American Mathematical Society, 1989. 18. O. Fujino. Semi-stable minimal model program for varieties with trivial canon- ical divisor. Proceedings of the Japan Academy, 87(3):25–30, 2011. 19. I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky. Hypergeometric func- ntions and toric varieties. (Russian) Funktsional. Anal. i Prilozhen, 23(2):12–26, 1989. 20. P.A. Griffiths, J.N. Mather, and E.M. Stein, editors. Topics in Transcendental Al- gebraic Geometry, volume 106 of Annals of Mathematics Studies. Princeton Uni- versity Press, 1984. 21. S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau. Mirror symmetry, mirror map and applications to calabi-yau hypersurfaces. Communications in Mathematical Physics, 167(2):301–350, 1995. 22. S. Hosono, B. H. Lian, and S.-T. Yau. Gkz-generalized hypergeometric systems in mirror symmetry of calabi-yau hypersurfaces. Communications in Mathemat- ical Physics, 182(3):535–577, 1996. 23. A. Huang, B. Lian, S.-T. Yau, and X. Zhu. Chain integral solutions to tautolog- ical systems. arXiv:1508.00406v2, 2015. 24. A. Huang, B. Lian, and X. Zhu. Period integrals and the Riemann-Hilbert cor- respondence. Inventiones Mathematicae, 2014. 25. M. Kashirawa. The asymptotic behavior of a variation of polarized Hodge structures. Publications of the Research Institute for Mathematical Science, 21:853– 875, 1985. 26. Y. Kawamata. Characterization of abelian varieties. Compositio Mathematica, 43(2):253–276, 1981. 27. Y. Kawamata. Deformations of canonical singularities. Journal of American Mathematics Society, 12(85-92), 1999. 28. Y. Kawamata. Variation of mixed Hodge structures and the positivity for al- gebraic fiber spaces. arXiv:1008.1489, 2010. 29. Y.-P. Lee, H.-W. Lin, and C.-L. Wang. Towards A + B theory in conifold tran- sitions for Calabi-Yau threefolds. arXiv:1502.03277, 2015. 30. B. Lian, R. Song, and S.-T. Yau. Periodic integrals and tautological systems. Jurnal of the European Mathematical Society, 14(4):1457–1483, 2013. 31. B. Lian and S.-T. Yau. Period integrals of CY and general type complete inter- sections. Inventiones Mathematicae, 191(1):35–89, January 2013. 32. Anvar R. Mavlyutov. Embedding of calabi-yau deformations into toric vari- eties. Mathematische Annalen, 333(1):45–65, 2005. 33. M. Reid. The moduli space of 3-folds with K = 0 may nevertheless be irre- ducible. Mathematische Annalen, 278:329–334, 1987. 34. W. Schmid. Variation of Hodge structure: The singularities of the period map- ping. Inventiones Mathematicae, 22:211–319, 1973. 35. J. Steenbrink. Limits of Hodge structures. Inventiones Mathematicae, 31(3):229– 257, 1976. 36. S. Takayama. On moderate degenerations of polarized Ricci-flat Kahler mani- folds. Kodaira Centennial issue of J. Math. Sci. Univ. Tokyo, 22:469–489, 2015. 37. G. Tian. Smoothness of the universal deformation space of compact Calabi– Yau manifolds and its Peterson–Weil metric. In S.-T. Yau, editor, Mathematical aspects of string theory, Advanced Series in Mathematical Physics. World Scien- tific Pub. Co. Inc. (April 1988), 1987. 38. A. Todorov. The Weil-Petersson geometry of the moduli space of SU(n ≥ 3) (Calabi–Yau) manifolds. Communications in Mathematical Physics, 126(2):325– 346, 1989. 39. V. Tosatti. Families of Calabi–Yau manifolds and canonical singularities. Inter- national Mathematics Research Notices, 2015. 40. C.-L. Wang. On the incompleteness of the Weil–Petersson metric along de- generations of Calabi–Yau manifolds. Mathematical Research Letter, 4:157–171, 1997. 41. C.-L. Wang. Quasi-Hodge metrics and canonical singularities. Mathematical Re- search Letter, 10(57-70), 2003. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50683 | - |
dc.description.abstract | We study the moduli space of polarized Calabi--Yau manifolds, especially degenerations of Calabi--Yau manifolds.
In the first part of the thesis, we give a Hodge theoretic criterion for a Calabi--Yau variety to have finite Weil--Petersson distance over higher dimensional bases up to a set of codimension $geq 2$ and a description on the codimension 2 locus for the moduli space of Calabi--Yau 3-folds. Also, we prove that the points lying on exactly one finite and one infinite divisor have infinite Weil--Petersson distance along angular slices and the points on the intersection of exact two infinite divisors have infinite distance measured by the metric induced from the dominant terms of the candidates of the Weil--Petersson potential. In the second part of the thesis, we study the degeneration of $mathcal{D}$-modules arsing from conifold transitions. Via the degeneration of Grassmannian manifolds $G(k,n)$ to Gorenstein toric Fano varieties $P(k,n)$, we suggest an approach to study the relation between the tautological systems on $G(k,n)$ and the (generalized) extended GKZ systems on the small resolution $hat{P}(k,n)$. We carry out the first but highly non-trivial case when $(k,n)=(2,4)$ to ensure its validity. To study the period integrals of Calabi--Yau complete intersections in $hat{P}(k,n)$, we also develop a new PDE system, which is a generalization of extended GKZ systems, governing the period integrals for the Calabi--Yau complete intersections in $hat{P}(k,n)$. We also establish a correspondence between the tautological systems on $G(2,5)$ and the generalized extended GKZ systems on $hat{P}(2,5)$. Finally, we also give an explicit description of the automorphism group of $P(k,n)$. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T12:52:28Z (GMT). No. of bitstreams: 1 ntu-105-F97221051-1.pdf: 1417037 bytes, checksum: 8e4a645a9f402b2f45ed1130c28a8884 (MD5) Previous issue date: 2016 | en |
dc.description.tableofcontents | 口試委員會審定書.................i
謝辭...................................iii 中文摘要.............................v Abstract............................vii Chapter 0. Introduction...........................................................1 Chapter 1. A Hodge theoretic criterion for finite Weil--Petersson degenerations over a higher dimensional base...............................................9 1. Statements of results and ideas of proofs........................9 2. Preliminaries...................................................................11 3. A finite distance criterion along boundary divisors.........15 4. Two parameter family of Calabi--Yau 3-folds.................21 5. Another aspect...............................................................39 Chapter 2. Tautological systems under conifold transitions on G(2,4)..............................................................45 1. Statements of results......................................................45 2. Preliminaries...................................................................47 3. Symmetry operators between G(2,4) and hat{P}(2,4)....55 4. Tautological systems on smooth toric varieties..............66 5. Tautological system on G(2,4) <=> Extended GKZ systems on hat{P}(2,4)...........................74 6. The case (k,n)=(2,5)........................................................80 7. Automorphisms of P(k,n)................................................84 Bibliography............................................................................91 | |
dc.language.iso | en | |
dc.title | 卡拉比--丘退化與過渡的週期幾何研究 | zh_TW |
dc.title | Geometry arising from periods of Calabi--Yau degenerations and transitions | en |
dc.type | Thesis | |
dc.date.schoolyear | 104-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 余正道(Jeng-Daw Yu),馬梓銘(Ziming Ma),程舜仁(Shun-Jen Cheng),何南國(Nan-Kuo Ho),吳思曄(Siye Wu) | |
dc.subject.keyword | 卡拉比--丘,模空間,韋--皮特森度量,錐過渡變換,自然方程組,擴展GKZ超幾何方程組, | zh_TW |
dc.subject.keyword | Calabi--Yau,moduli space,Weil--Petersson metric,conifold transitions,tautological systems,extended GKZ hypergeometric systems, | en |
dc.relation.page | 93 | |
dc.identifier.doi | 10.6342/NTU201601075 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2016-07-20 | |
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 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-105-1.pdf 目前未授權公開取用 | 1.38 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。