東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Intersection Theory of the Moduli Sp...

Kong, Bochao.

FindBook

Google Book

Amazon

博客來

Intersection Theory of the Moduli Space of Elliptic K3 Surfaces.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Intersection Theory of the Moduli Space of Elliptic K3 Surfaces./
作者:	Kong, Bochao.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2024,
面頁冊數:	135 p.
附註:	Source: Dissertations Abstracts International, Volume: 86-01, Section: B.
Contained By:	Dissertations Abstracts International86-01B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31300202
ISBN:	9798383219294

Intersection Theory of the Moduli Space of Elliptic K3 Surfaces.
Kong, Bochao.

Intersection Theory of the Moduli Space of Elliptic K3 Surfaces. - Ann Arbor : ProQuest Dissertations & Theses, 2024 - 135 p.

Source: Dissertations Abstracts International, Volume: 86-01, Section: B.

Thesis (Ph.D.)--University of California, San Diego, 2024.

Moduli spaces of K3 surfaces are fundamental objects in algebraic geometry. Elliptic K3 surfaces are K3 surfaces with elliptic fibration structure, and they are of particular interest due to their rich geometry. The moduli space of elliptic K3 surfaces can be studied using the theory of Weierstrass models. In this dissertation, we study the topology and intersection theory of the moduli space of elliptic K3 surfaces.We compute the Poincare polynomial of the moduli space of elliptic K3 surfaces. The main idea is constructing a compactification using the Weierstrass models, this compactification is a GIT quotient. We adapt Kirwan's blowup machinery to weighted projective space to compute the Poincare polynomial. We find the cohomology is mostly concentrated in the even degrees, but there is one odd degree class in degree 33.We also study the Chow ring of the moduli space of elliptic surfaces of degree N ≥ 2. We conclude that the Chow ring of the moduli space of elliptic surfaces is always generated by two classes. Furthermore, explicit relations between these classes are given, the Poincare polynomial for the Chow ring is the same for any N ≥ 2 and the ring is Gorenstein with socle in degree 16. When N = 2, we obtain the Chow ring for the moduli space of elliptic K3 surfaces, we conclude that the Chow ring in this case is tautological.Finally, we present localization computations on the relative Quot scheme over the moduli space of elliptic K3 surfaces. Our calculations are sufficient to determine the divisorial κ-classes in terms of the Hodge class. We also represent one Noether-Lefschetz divisor in terms of the Hodge class, which agrees with the modularity nature of the Noether-Lefschetz divisors.

ISBN: 9798383219294Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Intersection theory

Intersection Theory of the Moduli Space of Elliptic K3 Surfaces.
LDR:02883nmm a2200385 4500 001 2401639
005 20241022110543.5
006 m o d
007 cr#unu||||||||
008 251215s2024 ||||||||||||||||| ||eng d
020 $a 9798383219294
035 $a (MiAaPQ)AAI31300202
035 $a AAI31300202
035 $a 2401639
040 $a MiAaPQ $c MiAaPQ
100 1 $a Kong, Bochao. $3 3771738
245 1 0 $a Intersection Theory of the Moduli Space of Elliptic K3 Surfaces.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 135 p.
500 $a Source: Dissertations Abstracts International, Volume: 86-01, Section: B.
500 $a Advisor: Oprea, Dragos.
502 $a Thesis (Ph.D.)--University of California, San Diego, 2024.
520 $a Moduli spaces of K3 surfaces are fundamental objects in algebraic geometry. Elliptic K3 surfaces are K3 surfaces with elliptic fibration structure, and they are of particular interest due to their rich geometry. The moduli space of elliptic K3 surfaces can be studied using the theory of Weierstrass models. In this dissertation, we study the topology and intersection theory of the moduli space of elliptic K3 surfaces.We compute the Poincare polynomial of the moduli space of elliptic K3 surfaces. The main idea is constructing a compactification using the Weierstrass models, this compactification is a GIT quotient. We adapt Kirwan's blowup machinery to weighted projective space to compute the Poincare polynomial. We find the cohomology is mostly concentrated in the even degrees, but there is one odd degree class in degree 33.We also study the Chow ring of the moduli space of elliptic surfaces of degree N ≥ 2. We conclude that the Chow ring of the moduli space of elliptic surfaces is always generated by two classes. Furthermore, explicit relations between these classes are given, the Poincare polynomial for the Chow ring is the same for any N ≥ 2 and the ring is Gorenstein with socle in degree 16. When N = 2, we obtain the Chow ring for the moduli space of elliptic K3 surfaces, we conclude that the Chow ring in this case is tautological.Finally, we present localization computations on the relative Quot scheme over the moduli space of elliptic K3 surfaces. Our calculations are sufficient to determine the divisorial κ-classes in terms of the Hodge class. We also represent one Noether-Lefschetz divisor in terms of the Hodge class, which agrees with the modularity nature of the Noether-Lefschetz divisors.
590 $a School code: 0033.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Intersection theory
653 $a Moduli spaces
653 $a Poincare polynomial
653 $a Weierstrass models
653 $a Cohomology
690 $a 0405
690 $a 0642
710 2 $a University of California, San Diego. $b Mathematics. $3 1022364
773 0 $t Dissertations Abstracts International $g 86-01B.
790 $a 0033
791 $a Ph.D.
792 $a 2024
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31300202