2期

最新文章

• Diffeomorphism groups of critical regularity AI翻译
  作者：Kim, Sang-hyun; Koberda, Thomas
  作者单位：Korea Institute for Advanced Study (KIAS); University of Virginia
  摘要：Let M be a circle or a compact interval, and let alpha = k + tau >= 1 be a real number such that k = [alpha]. We write Diff(+)(alpha)(M) for the group of orientation preserving C-k diffeomorphisms of M whose kth derivatives are Holder continuous with exponent tau. We prove that there exists a continuum of isomorphism types of finitely generated subgroups G <= Diff(+)(alpha)(M) with the property that G admits no injective homomorphisms into boolean OR(beta>alpha) Diff(+)(beta)(M). We also show ...
• A counterexample to the weak density of smooth maps between manifolds in Sobolev spaces AI翻译
  作者：Bethuel, Fabrice
  作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
  摘要：The present paper presents a counterexample to the sequential weak density of smooth maps between two manifolds M and N in the Sobolev space W-1,W-p(M, N), in the case p is an integer. It has been shown (see e.g. Bethuel in Acta Math 167:153-206, 1991) that, if p < dim M is not an integer and the [p]-th homotopy group pi([p])(N) of N is not trivial, [p] denoting the largest integer less then p, then smooth maps are not sequentially weakly dense in W-1,W-p(M, N). On the other hand, in the case ...
• Singularities and syzygies of secant varieties of nonsingular projective curves AI翻译
  作者：Ein, Lawrence; Niu, Wenbo; Park, Jinhyung
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Arkansas System; University of Arkansas Fayetteville; Sogang University
  摘要：In recent years, the equations defining secant varieties and their syzygies have attracted considerable attention. The purpose of the present paper is to conduct a thorough study on secant varieties of curves by settling several conjectures and revealing interaction between singularities and syzygies. The main results assert that if the degree of the embedding line bundle of a nonsingular curve of genusgis greater than 2g+2k+p for nonnegative integerskandp, then thek-th secant variety of the c...
• Pathologies on the Hilbert scheme of points AI翻译
  作者：Jelisiejew, Joachim
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
  摘要：We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we show that Vakil's Murphy's Law holds up to retraction for this scheme. Our main tool is a generalized version of the Bialynicki-Birula decomposition.
• Birational geometry of symplectic quotient singularities AI翻译
  作者：Bellamy, Gwyn; Craw, Alastair
  作者单位：University of Glasgow; University of Bath
  摘要：For a finite subgroup Gamma subset of SL(2,C)Gamma \subset \mathrm {SL}(2,\mathbb {C})$$\end{document} and for n >= 1, we use variation of GIT quotient for Nakajima quiver varieties to study the birational geometry of the Hilbert scheme of n points on the minimal resolution S of the Kleinian singularity C2/Gamma. It is well known that X:=Hilb[n](S)is a projective, crepant resolution of the symplectic singularity C2n/Gamma n\ where Gamma n=Gamma wreath product Sn is the wreath product. We prove...
• Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice AI翻译
  作者：Ding, Jian; Smart, Charles K.
  作者单位：University of Pennsylvania; University of Chicago
  摘要：We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent on a large square is likely to decay exponentially. This implies almost sure Anderson localization for energies sufficiently close to the edge of the spectrum. Our proof follows the program of Bourgain-Kenig, using a new unique continuation result inspired by a Liouville theorem of Buhovsky-Logunov-...
• A non-nuclear C*-algebra with the weak expectation property and the local lifting property AI翻译
  作者：Pisier, Gilles
  作者单位：Texas A&M University System; Texas A&M University College Station
  摘要：We construct the first example of a C*-algebra A with the properties in the title. This gives a new example of non-nuclear A for which there is a unique C*-norm on A circle times A(op). This example is of particular interest in connection with the Connes-Kirchberg problem, which is equivalent to the question whether C* (F-2), which is known to have the LLP, also has the WEP. Our C*-algebra A has the same collection of finite dimensional operator subspaces as C* (F-2) or C* (F-infinity). In add...
• Differential K-theory and localization formula for η-invariants AI翻译
  作者：Liu, Bo; Ma, Xiaonan
  作者单位：East China Normal University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Chinese Academy of Sciences; University of Science & Technology of China, CAS
  摘要：In this paper we obtain a localization formula in differential K-theory for S-1-actions. We establish a localization formula for equivariant eta-invariants by combining this result with our extension of Goette's result on the comparison of two types of equivariant eta-invariants. An important step in our approach is to construct a pre-lambda-ring structure in differential K-theory.
• A nonlinear Plancherel theorem with applications to global well-posedness for the defocusing Davey-Stewartson equation and to the inverse boundary value problem of Calderon AI翻译
  作者：Nachman, Adrian; Regev, Idan; Tataru, Daniel
  作者单位：University of Toronto; University of California System; University of California Berkeley
  摘要：We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in L2 for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calderon in dimension 2, for conductivities sigma>0 with log sigma is an element of H1. The proof of the nonlinear Plancherel theorem includes...
• Categorical smooth compactifications and generalized Hodge-to-de Rham degeneration AI翻译
  作者：Efimov, Alexander, I
  作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; HSE University (National Research University Higher School of Economics)
  摘要：We disprove two (unpublished) conjectures of Kontsevich which state generalized versions of categorical Hodge-to-de Rham degeneration for smooth and for proper DG categories (but not smooth and proper, in which case degeneration is proved by Kaledin (in: Algebra, geometry, and physics in the 21st century. Birkhauser/Springer, Cham, pp 99-129, 2017). In particular, we show that there exists a minimal 10-dimensional A infinity-algebra over a field of characteristic zero, for which the supertrace...