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Date
2023-07Type
- Journal Article
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yes
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Abstract
Let E_N denote the coarse moduli space of smooth elliptic surfaces over P¹ with fundamental invariant N. We compute the Chow ring A∗(E_N) for N ⩾ 2. For each N ⩾ 2, A∗(E_N) is Gorenstein with socle in codimension 16, which is surprising in light of the fact that the dimension of EN is 10N −2. As an application, we show that the maximal dimension of a complete subvariety of E_N is 16. When N = 2, the corresponding elliptic surfaces are K3 surfaces polarized by a hyperbolic lattice U. We show that the generators for A∗(E_2) are tautological classes on the moduli space FU of U-polarized K3 surfaces, which provides evidence for a conjecture of Oprea and Pandharipande on the tautological rings of moduli spaces of lattice polarized K3 surfaces. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000665233Publication status
publishedJournal / series
Algebraic GeometryVolume
Pages / Article No.
Publisher
Foundation Compositio MathematicaSubject
Chow ring; elliptic surfaces; moduli of K3 surfacesMore
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ETH Bibliography
yes
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