Inventiones mathematicae

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• Group actions, corks and exotic smoothings of R4 AI翻译
  作者：Gompf, Robert E.
  作者单位：University of Texas System; University of Texas Austin
  摘要：We provide the first information on diffeotopy groups of exotic smoothings of R-4: For each of uncountably many smoothings, there are uncountably many isotopy classes of self-diffeomorphisms. We realize these by various explicit group actions. There are also actions at infinity by non-finitely generated groups, for which no nontrivial element extends over the whole manifold. In contrast, every diffeomorphism of the end of the universal R4 extends. Our techniques apply to many other open 4-mani...
• The Galois action on geometric lattices and the mod- I/OM AI翻译
  作者：Topaz, Adam
  作者单位：University of Oxford
  摘要：This paper studies the Galois action on a special lattice of geometric origin, which is related to mod- abelian-by-central quotients of geometric fundamental groups of varieties. As a consequence, we formulate and prove the mod- abelian-by-central variant/strengthening of a conjecture due to Ihara/Oda-Matsumoto.
• A projective variety with discrete, non-finitely generated automorphism group AI翻译
  作者：Lesieutre, John
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
  摘要：We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.
• Exponential decay of correlations for finite horizon Sinai billiard flows AI翻译
  作者：Baladi, Viviane; Demers, Mark F.; Liverani, Carlangelo
  作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Fairfield University; University of Rome Tor Vergata
  摘要：We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L-t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions.
• On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad AI翻译
  作者：Beuzart-Plessis, Raphael
  作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：We prove an integral formula computing multiplicities of square-integrable representations relative to Galois pairs over p-adic fields and we apply this formula to verify two consequences of a conjecture of Dipendra Prasad. One concerns the exact computation of the multiplicity of the Steinberg representation and the other the invariance of multiplicities by transfer among inner forms.
• Holomorphic anomaly equations and the Igusa cusp form conjecture AI翻译
  作者：Oberdieck, Georg; Pixton, Aaron
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：Let S be a K3 surface and let E be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold for all curve classes which are primitive in the K3 factor. In particular, we deduce the Igusa cusp form conjecture. The proof relies on new results in the Gromov-Witten theory of elliptic curves and K3 surfaces. We show the generating series of Gromov-Witten classes of an elliptic curve are cycle-valued quasimodular forms and satisfy a holomorphic anomaly equation. The q...
• Orbit spaces of unimodular rows over smooth real affine algebras AI翻译
  作者：Das, Mrinal Kanti; Tikader, Soumi; Zinna, Md. Ali
  作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; National Institute of Science Education & Research (NISER)
• Sampling theorems for shift-invariant spaces, Gabor frames, and totally positive functions AI翻译
  作者：Groechenig, Karlheinz; Romero, Jose Luis; Stoeckler, Joachim
  作者单位：University of Vienna; Dortmund University of Technology; Austrian Academy of Sciences
  摘要：We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as for (in which case g is called totally positive of Gaussian type). In analogy to Beurling's sampling theorem for the Paley-Wiener space of entire functions, we prove that every separated set with lower Beurling density is a sampling set for the shift-invariant space generated by such a g. In view of the known nece...
• Mean dimension of the dynamical system of Brody curves AI翻译
  作者：Tsukamoto, Masaki
  作者单位：Kyoto University
  摘要：Mean dimension is a topological invariant of dynamical systems counting the number of parameters averaged by dynamics. Brody curves are Lipschitz holomorphic maps , and they form an infinite dimensional dynamical system. Gromov started the problem of estimating its mean dimension in 1999. We solve this problem by proving the exact mean dimension formula. Our formula expresses the mean dimension by the energy density of Brody curves. As a key novel ingredient, we use an information theoretic ap...
• A decomposition theorem for singular spaces with trivial canonical class of dimension at most five AI翻译
  作者：Druel, Stephane
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite cover, ,tale in codimension one, that decomposes as a product of an Abelian variety, and singular analogues of irreducible Calabi-Yau and irreducible holomorphic symplectic varieties.