https://scholars.lib.ntu.edu.tw/handle/123456789/638949
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.author | Chen, Zhijie | en_US |
dc.contributor.author | CHANG-SHOU LIN | en_US |
dc.date.accessioned | 2024-01-26T06:45:14Z | - |
dc.date.available | 2024-01-26T06:45:14Z | - |
dc.date.issued | 2023-09-01 | - |
dc.identifier.issn | 0022040X | - |
dc.identifier.uri | https://scholars.lib.ntu.edu.tw/handle/123456789/638949 | - |
dc.description.abstract | We study the SU(3) Toda system with singular sources (∆ ∆ u v+ + 2 2 e e vu− − e e uv= = 4 4 π π PPm kmk=0 =0 n n 2 1 ,k,k δ δ p p k kon on E E τ τ, , where Eτ := C/(Z + Zτ) with Im τ > 0 is a flat torus, δpk is the Dirac measure at pk, and ni,k ∈ Z≥0 satisfy Pk n1,k 6≡ Pk n2,k mod 3. This is known as the non-critical case and it follows from a general existence result of [3] that solutions always exist. In this paper we prove that (i) The system has at most m 1 3 × 2m+1Y (n1,k + 1)(n2,k + 1)(n1,k + n2,k + 2) ∈ N k=0 solutions. We have several examples to indicate that this upper bound should be sharp. Our proof presents a nice combination of the apriori estimates from analysis and the classical Bézout theorem from algebraic geometry. (ii) For m = 0 and p0 = 0, the system has even solutions if and only if at least one of {n1,0, n2,0} is even. Furthermore, if n1,0 is odd, n2,0 is even and n1,0 < n2,0, then except for finitely many τ’s modulo SL(2, Z) action, the system has exactly n1,20+1 even solutions. Differently from [3], our proofs are based on the integrability of the Toda system, and also imply a general non-existence result for even solutions of the Toda system with four singular sources. | en_US |
dc.relation.ispartof | Journal of Differential Geometry | en_US |
dc.title | ON NUMBER AND EVENNESS OF SOLUTIONS OF THE SU(3) TODA SYSTEM ON FLAT TORI WITH NON-CRITICAL PARAMETERS | en_US |
dc.type | journal article | en |
dc.identifier.doi | 10.4310/jdg/1695236592 | - |
dc.identifier.scopus | 2-s2.0-85174735428 | - |
dc.identifier.url | https://api.elsevier.com/content/abstract/scopus_id/85174735428 | - |
dc.relation.journalvolume | 125 | en_US |
dc.relation.journalissue | 1 | en_US |
dc.relation.pageend | 120 | en_US |
item.openairetype | journal article | - |
item.openairecristype | http://purl.org/coar/resource_type/c_6501 | - |
item.fulltext | no fulltext | - |
item.grantfulltext | none | - |
item.cerifentitytype | Publications | - |
crisitem.author.dept | Mathematics | - |
crisitem.author.dept | Center for Advanced Study in Theoretical Sciences (CASTS) | - |
crisitem.author.orcid | 0000-0001-7446-0251 | - |
crisitem.author.parentorg | College of Science | - |
crisitem.author.parentorg | Others: University-Level Research Centers | - |
顯示於: | 數學系 |
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