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Intersection Theory of the Moduli Space of Elliptic K3 Surfaces.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Intersection Theory of the Moduli Space of Elliptic K3 Surfaces./
作者:	Kong, Bochao.
面頁冊數:	1 online resource (135 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-01, Section: B.
Contained By:	Dissertations Abstracts International86-01B.
標題:	Mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9798383219294

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

Intersection Theory of the Moduli Space of Elliptic K3 Surfaces. - 1 online resource (135 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798383219294Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Intersection theoryIndex Terms--Genre/Form:

554714
Electronic books.

Intersection Theory of the Moduli Space of Elliptic K3 Surfaces.
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504 $a Includes bibliographical references
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.
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653 $a Moduli spaces
653 $a Poincare polynomial
653 $a Weierstrass models
653 $a Cohomology
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