-
作者：Blum, Harold; Xu, Chenyang
摘要：We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is separated. Together with recently proven boundedness and openness statements, the latter result yields a separated Deligne-Mumford stack parametrizing all uniformly K-stable Q-Fano varieties of fixed dimension and volume. The result also implies that the automorphism group of a K-stable Q-Fano variety is finite.
-
作者：Gao, Ziyang; Habegger, Philipp
摘要：On an abelian scheme over a smooth curve over (Q) over bar a symmetric relatively ample line bundle defines a fiberwise Neron-Tate height. If the base curve is inside a projective space, we also have a height on its (Q) over bar -points that serves as a measure of each fiber, an abelian variety. Silverman proved an asymptotic equality between these two heights on a curve in the abelian scheme. In this paper we prove an inequality between these heights on a subvariety of any dimension of the ab...
-
作者：Rondigs, Oliver; Spitzweck, Markus; Ostvaer, Paul Arne
摘要：We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice spectral sequence.
-
作者：Zemke, Ian
摘要：We prove that the map on knot Floer homology induced by a ribbon concordance is injective. As a consequence, we prove that the Seifert genus is monotonic under ribbon concordance. Generalizing theorems of Gabai and Scharlemann, we also prove that the Seifert genus is super-additive under band connected sums of arbitrarily many knots. Our results give evidence for a conjecture of Gordon that ribbon concordance is a partial order on the set of knots.
-
作者：Du, Xiumin; Zhang, Ruixiang
摘要：We show that, for n >= 3, limt(t -> 0) e(it Delta) f (x) = f (x) holds almost everywhere for all f is an element of H-s (R-n) provided that s > n/2(n+1). Due to a counterexample by Bourgain, up to the endpoint, this result is sharp and fully resolves a problem raised by Carleson. Our main theorem is a fractal L-2 restriction estimate, which also gives improved results on the size of the divergence set of the Schrodinger solutions, the Falconer distance set problem and the spherical average Fou...
-
作者：Prywes, Eden
摘要：We show that a closed, connected and orientable Riemannian manifold M of dimension d that admits a nonconstant quasiregular mapping from R-d must have bounded dimension of the cohomology independent of the distortion of the map. The dimension of the degree l de Rham cohomology of M is bounded above by ((d)(l)). This is a sharp upper bound that proves the Bonk-Heinonen conjecture. A corollary of this theorem answers an open problem posed by Gromov in 1981. He asked whether there exists a d-dime...
-
作者：Schneiderman, Rob; Teichner, Peter
摘要：We compute the group LM2,24 of link homotopy classes of link maps of two 2-spheres into 4-space. It turns out to be free abelian, generated by geometric constructions applied to the Fenn-Rolfsen link map and detected by two self-intersection invariants introduced by Kirk in this setting. As a corollary, we show that any link map with one topologically embedded component is link homotopic to the unlink. Our proof introduces a new basic link homotopy, which we call a Whitney homotopy, that shrin...
-
作者：Anantharaman, Nalini; Sabri, Mostafa
摘要：We prove a quantum-ergodicity theorem on large graphs, for eigenfunctions of Schrodinger operators in a very general setting. We consider a sequence of finite graphs endowed with discrete Schrodinger operators, assumed to have a local weak limit. We assume that our graphs have few short loops, in other words that the limit model is a random rooted tree endowed with a random discrete Schrodinger operator. We show that an absolutely continuous spectrum for the infinite model, reinforced by a goo...
-
作者：Gamburd, Alex; Magee, Michael; Ronan, Ryan
摘要：We establish an asymptotic formula for the number of integer solutions to the Markoff-Hurwitz equation x(1)(2) + x(2)(2) + ... +x(n)(2) = ax(1)x(2) ... x(n) + k. When n >= 4, the previous best result is by Baragar (1998) that gives an exponential rate of growth with exponent beta that is not in general an integer when n >= 4. We give a new interpretation of this exponent of growth in terms of the unique parameter for which there exists a certain conformal measure on projective space.
-
作者：Luk, Jonathan; Oh, Sung-Tin
摘要：This is the first and main paper of a two-part series, in which we prove the C-2-formulation of the strong cosmic censorship conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry for two-ended asymptotically flat data. For this model, it is known through the works of Dafermos and Dafermos-Rodnianski that the maximal globally hyperbolic future development of any admissible two-ended asymptotically flat Cauchy initial data set possesses a non-empty Cauchy horizon, ...
