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作者：Dolgushev, V. A.; Rogers, C. L.; Willwacher, T. H.
摘要：We generalize Kontsevich's construction of L-infinity-derivations of polyvector fields from the affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph complex to the deformation complex of the sheaf of polyvector fields on a smooth algebraic variety. We show that the action of Deligne-Drinfeld elements of the Grothendieck-Teichmuller Lie algebra on the cohomology of the sheaf of polyvector fields coincides wi...
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作者：Marcus, Adam W.; Spielman, Daniel A.; Srivastava, Nikhil
摘要：We prove that there exist infinite families of regular bipartite Ramanujan graphs of every degree bigger than 2. We do this by proving a variant of a conjecture of Bilu and Linial about the existence of good 2-lifts of every graph. We also establish the existence of infinite families of irregular Ramanujan graphs, whose eigenvalues are bounded by the spectral radius of their universal cover. Such families were conjectured to exist by Linial and others. In particular, we prove the existence of ...
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作者：Maynard, James
摘要：We introduce a refinement of the GPY sieve method for studying prime k-tuples and small gaps between primes. This refinement avoids previous limitations of the method and allows us to show that for each k, the prime k-tuples conjecture holds for a positive proportion of admissible k-tuples. In particular, lim inf(n)(p(n)+(m) - p(n)) < infinity for every integer m. We also show that lim inf(p(n)+(l) - pn) <= 600 and, if we assume the Elliott-Halberstam conjecture, that lim inf(n) (p(n)+(1) - p(...
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作者：Guan, Qi'an; Zhou, Xiangyu
摘要：In this article, we solve the strong openness conjecture on the multiplier ideal sheaf associated to any plurisubharmonic function, which was posed by Demailly.
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作者：Einsiedler, Manfred; Lindenstrauss, Elon
摘要：We classify invariant and ergodic probability measures on arithmetic homogeneous quotients of semisimple S-algebraic groups invariant under a maximal split torus in at least one simple local factor and show that the algebraic support of such a measure splits into the product of four homogeneous spaces: a torus, a homogeneous space on which the measure is (up to finite index) the Haar measure, a product of homogeneous spaces on each of which the action degenerates to a rank one action, and a ho...
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作者：Bramham, Barney
摘要：We prove that every C-infinity-srnooth, area preserving diffeomorphisrn of the closed 2-disk having not more than one periodic point is the uniform limit of periodic C-infinity-srnooth diffeomorphisrns. In particular, every smooth irrational pseudo-rotation can be C-0-approximated by integrable systems. This partially answers a long standing question of A. Katok regarding zero entropy Hamiltonian systems in low dimensions. Our approach uses pseudoholomorphic curve techniques from symplectic ge...
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作者：Roulleau, Xavier; Urzua, Giancarlo
摘要：We prove that for any number r is an element of [2,3], there are spin (resp. non-spin and minimal) simply connected complex surfaces of general type X with c(1)(2)(X)/c(2)(X) arbitrarily close to r. In particular, this shows the existence of simply connected surfaces of general type arbitrarily close to the Bogomolov-Miyaoka-Yau line. In addition, we prove that for any r is an element of [1,3] and any integer q >= 0, there are minimal complex surfaces of general type X with C-1(2)(X)/c(2)(X) a...
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作者：Roy, Damien
摘要：Recently, W. M. Schmidt and L. Summerer introduced a new theory which allowed them to recover the main known inequalities relating the usual exponents of Diophantine approximation to a point in \mathbb{R}boolean AND n, and to discover new ones. They first note that these exponents can be computed in terms of the successive minima of a parametric family of convex bodies attached to the given point. Then they prove that the n-tuple of these successive minima can in turn be approximated up to bou...
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作者：Globevnik, Josip
摘要：In 1977, P. Yang asked whether there exist complete immersed complex submanifolds phi: M-k -> C-N with bounded image. A positive answer is known for holomorphic curves (k = 1) and partial answers are known for the case when k > 1. The principal result of the present paper is a construction of a holomorphic function on the open unit ball B-N of C-N whose real part is unbounded on every path in B-N of finite length that ends on bB(N). A consequence is the existence of a complete, closed complex ...
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作者：Andersson, Lars; Blue, Pieter
摘要：Energy and decay estimates for the wave equation on the exterior region of slowly rotating Kerr spacetimes are proved. The method used is a generalisation of the vector-field method that allows the use of higher-order symmetry operators. In particular, our method makes use of the second-order Carter operator, which is a hidden symmetry in the sense that it does not correspond to a Killing symmetry of the spacetime.
