Arithmetic of the moduli of semistable elliptic surfaces
DC Field | Value | Language |
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dc.contributor.author | Han C. | - |
dc.contributor.author | Jun-Yong Park | - |
dc.date.available | 2020-01-31T00:56:25Z | - |
dc.date.created | 2019-05-29 | - |
dc.date.issued | 2019-04 | - |
dc.identifier.issn | 0025-5831 | - |
dc.identifier.uri | https://pr.ibs.re.kr/handle/8788114/6930 | - |
dc.description.abstract | © 2019, Springer-Verlag GmbH Germany, part of Springer Nature. We prove a new sharp asymptotic with the lower order term of zeroth order on ZFq(t)(B) for counting the semistable elliptic curves over F q (t) by the bounded height of discriminant Δ (X). The precise count is acquired by considering the moduli of nonsingular semistable elliptic fibrations over P 1 , also known as semistable elliptic surfaces, with 12n nodal singular fibers and a distinguished section. We establish a bijection of K-points between the moduli functor of semistable elliptic surfaces and the stack of morphisms L 1 , 12 n ≅ Hom n (P 1 , M¯ 1 , 1 ) where M¯ 1 , 1 is the Deligne–Mumford stack of stable elliptic curves and K is any field of characteristic ≠ 2 , 3. For char (K) = 0 , we show that the class of Hom n (P 1 , P(a, b)) in the Grothendieck ring of K–stacks, where P(a, b) is a 1-dimensional (a, b) weighted projective stack, is equal to L ( a + b ) n + 1 - L ( a + b ) n - 1 . Consequently, we find that the motive of the moduli L 1 , 12 n is L 10 n + 1 - L 10 n - 1 and the cardinality of the set of weighted F q -points to be # q (L 1 , 12 n ) = q 10 n + 1 - q 10 n - 1 . In the end, we formulate an analogous heuristic on Z Q (B) for counting the semistable elliptic curves over Q by the bounded height of discriminant Δ through the global fields analogy | - |
dc.language | 영어 | - |
dc.publisher | SPRINGER | - |
dc.title | Arithmetic of the moduli of semistable elliptic surfaces | - |
dc.type | Article | - |
dc.type.rims | ART | - |
dc.identifier.wosid | 000492595100024 | - |
dc.identifier.scopusid | 2-s2.0-85064609746 | - |
dc.identifier.rimsid | 68023 | - |
dc.contributor.affiliatedAuthor | Jun-Yong Park | - |
dc.identifier.doi | 10.1007/s00208-019-01830-7 | - |
dc.identifier.bibliographicCitation | MATHEMATISCHE ANNALEN, v.28, no.2, pp.183 - 215 | - |
dc.relation.isPartOf | MATHEMATISCHE ANNALEN | - |
dc.citation.title | MATHEMATISCHE ANNALEN | - |
dc.citation.volume | 28 | - |
dc.citation.number | 2 | - |
dc.citation.startPage | 183 | - |
dc.citation.endPage | 215 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | CURVES | - |
dc.subject.keywordPlus | STABILITY | - |
dc.subject.keywordPlus | TOPOLOGY | - |
dc.subject.keywordPlus | STACKS | - |
dc.subject.keywordPlus | SPACES | - |