FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2111243681> ?p ?o ?g. }

• W2111243681 endingPage "rnw105" @default.
• W2111243681 startingPage "rnw105" @default.
• W2111243681 abstract "The stack ℳ¯g,n of stable curves and its coarse moduli space M¯g,n are defined over ℤ⁠, and therefore over any field. Over an algebraically closed field of characteristic zero, in [11] Hacking showed that ℳ¯g,n is rigid (a conjecture of Kapranov), in [2, 23] Bruno and Mella for g=0⁠, and the second author for g≥1 showed that its automorphism group is the symmetric group Sn⁠, permuting marked points unless (g,n)∈{(0,4),(1,1),(1,2)}⁠. The methods used in the papers above do not extend to positive characteristic. We show that in characteristic p>0⁠, the rigidity of ℳ¯g,n⁠, with the same exceptions as over ℂ⁠, implies that its automorphism group is Sn⁠. We prove that, over any field, M¯0,n is rigid and deduce that, over any field, Aut(M¯0,n)≅Sn for n≥5⁠. Going back to characteristic zero, we prove that for g+n>4⁠, the coarse moduli space M¯g,n is rigid, extending a result of Hacking who had proven it has no locally trivial deformations. Finally, we show that M¯1,2 is not rigid, although it does not admit locally trivial deformations, by explicitly computing his Kuranishi family. The stack ℳ¯g,n parametrizing Deligne–Mumford stable curves and its coarse moduli space M¯g,n are among the most fascinating and widely studied objects in algebraic geometry. A remarkable property of ℳ¯g,n is that it is smooth and proper over Spec(ℤ)⁠, and thus ℳ¯g,nR is defined over any commutative ring R via base change ... By [18] the formation of the coarse moduli space is compatible with flat base change; we write M¯g,nR for the coarse moduli scheme of ℳ¯g,nR⁠. The symmetric group Sn acts via permutations of the marked points on M¯g,nR and ℳ¯g,nR for every ring R⁠. The biregular automorphisms of the moduli space Mg,n⁠, and of its Deligne–Mumford compactification M¯g,n have been studied in a series of papers [2, 9, 21-26, 33]. It is known that, with a short and explicit list of exceptions, over the field of complex numbers both the automorphism groups of the stack and of the coarse moduli space are isomorphic to Sn⁠, see Appendix for details. In Section 2 we first study how automorphisms of a scheme behave with respect to field extensions, and then, given a scheme X→Spec(A) over a local ring A with residue field K and generic point ξ∈Spec(A)⁠, we show how the infinitesimal rigidity of XK plays a fundamental role in lifting automorphisms of XK to automorphisms of Xξ⁠. Finally, in Section 7 we apply these results together with the rigidity results in Section 4 to M¯0,nK⁠, with K a field of positive characteristic and A=W(K) the ring of Witt vector over K⁠, in order to compute the automorphism group of M¯0,nK⁠. The main results on the automorphism groups in Proposition 5.4, Theorem 7.3, and Appendix can be summarized as follows:" @default.
• W2111243681 created "2016-06-24" @default.
• W2111243681 creator A5064211398 @default.
• W2111243681 creator A5082388083 @default.
• W2111243681 date "2016-06-14" @default.
• W2111243681 modified "2023-10-01" @default.
• W2111243681 title "On the rigidity of moduli of curves in arbitrary characteristic" @default.
• W2111243681 cites W1480220833 @default.
• W2111243681 cites W1507919071 @default.
• W2111243681 cites W1550991113 @default.
• W2111243681 cites W1574682256 @default.
• W2111243681 cites W1979153357 @default.
• W2111243681 cites W1985174140 @default.
• W2111243681 cites W2000851731 @default.
• W2111243681 cites W2033693626 @default.
• W2111243681 cites W2055722844 @default.
• W2111243681 cites W2055803666 @default.
• W2111243681 cites W2068569397 @default.
• W2111243681 cites W2583112400 @default.
• W2111243681 cites W2598863526 @default.
• W2111243681 cites W2963822086 @default.
• W2111243681 cites W2964002033 @default.
• W2111243681 cites W2964290280 @default.
• W2111243681 cites W4205502224 @default.
• W2111243681 cites W4241195498 @default.
• W2111243681 cites W4248269519 @default.
• W2111243681 cites W4248533608 @default.
• W2111243681 cites W954650338 @default.
• W2111243681 doi "https://doi.org/10.1093/imrn/rnw105" @default.
• W2111243681 hasPublicationYear "2016" @default.
• W2111243681 type Work @default.
• W2111243681 sameAs 2111243681 @default.
• W2111243681 citedByCount "6" @default.
• W2111243681 countsByYear W21112436812014 @default.
• W2111243681 countsByYear W21112436812016 @default.
• W2111243681 countsByYear W21112436812017 @default.
• W2111243681 countsByYear W21112436812019 @default.
• W2111243681 countsByYear W21112436812021 @default.
• W2111243681 crossrefType "journal-article" @default.
• W2111243681 hasAuthorship W2111243681A5064211398 @default.
• W2111243681 hasAuthorship W2111243681A5082388083 @default.
• W2111243681 hasBestOaLocation W21112436812 @default.
• W2111243681 hasConcept C114614502 @default.
• W2111243681 hasConcept C118712358 @default.
• W2111243681 hasConcept C121089165 @default.
• W2111243681 hasConcept C121332964 @default.
• W2111243681 hasConcept C138885662 @default.
• W2111243681 hasConcept C160343418 @default.
• W2111243681 hasConcept C199360897 @default.
• W2111243681 hasConcept C202444582 @default.
• W2111243681 hasConcept C203701370 @default.
• W2111243681 hasConcept C2780813799 @default.
• W2111243681 hasConcept C2780990831 @default.
• W2111243681 hasConcept C2781311116 @default.
• W2111243681 hasConcept C33923547 @default.
• W2111243681 hasConcept C41008148 @default.
• W2111243681 hasConcept C41895202 @default.
• W2111243681 hasConcept C62520636 @default.
• W2111243681 hasConcept C73373263 @default.
• W2111243681 hasConcept C9395851 @default.
• W2111243681 hasConceptScore W2111243681C114614502 @default.
• W2111243681 hasConceptScore W2111243681C118712358 @default.
• W2111243681 hasConceptScore W2111243681C121089165 @default.
• W2111243681 hasConceptScore W2111243681C121332964 @default.
• W2111243681 hasConceptScore W2111243681C138885662 @default.
• W2111243681 hasConceptScore W2111243681C160343418 @default.
• W2111243681 hasConceptScore W2111243681C199360897 @default.
• W2111243681 hasConceptScore W2111243681C202444582 @default.
• W2111243681 hasConceptScore W2111243681C203701370 @default.
• W2111243681 hasConceptScore W2111243681C2780813799 @default.
• W2111243681 hasConceptScore W2111243681C2780990831 @default.
• W2111243681 hasConceptScore W2111243681C2781311116 @default.
• W2111243681 hasConceptScore W2111243681C33923547 @default.
• W2111243681 hasConceptScore W2111243681C41008148 @default.
• W2111243681 hasConceptScore W2111243681C41895202 @default.
• W2111243681 hasConceptScore W2111243681C62520636 @default.
• W2111243681 hasConceptScore W2111243681C73373263 @default.
• W2111243681 hasConceptScore W2111243681C9395851 @default.
• W2111243681 hasLocation W21112436811 @default.
• W2111243681 hasLocation W21112436812 @default.
• W2111243681 hasLocation W21112436813 @default.
• W2111243681 hasOpenAccess W2111243681 @default.
• W2111243681 hasPrimaryLocation W21112436811 @default.
• W2111243681 hasRelatedWork W1500759486 @default.
• W2111243681 hasRelatedWork W1550991113 @default.
• W2111243681 hasRelatedWork W2167154330 @default.
• W2111243681 hasRelatedWork W2236139491 @default.
• W2111243681 hasRelatedWork W2902048235 @default.
• W2111243681 hasRelatedWork W3080860077 @default.
• W2111243681 hasRelatedWork W4221156743 @default.
• W2111243681 hasRelatedWork W4225993373 @default.
• W2111243681 hasRelatedWork W4289147182 @default.
• W2111243681 hasRelatedWork W4298098124 @default.
• W2111243681 isParatext "false" @default.
• W2111243681 isRetracted "false" @default.
• W2111243681 magId "2111243681" @default.
• W2111243681 workType "article" @default.