Manuscripta Mathematica最新文献

We show that the p-adic Siegel–Eisenstein series of general degree attached to two kind of number sequences are both linear combinations of genus theta series of level dividing p, by applying the theory of mod p-power singular forms. As special cases of this result, we derive the results of Nagaoka and Katsurada–Nagaoka.

We show an equation of Euler characteristics of tautological sheaves on Hilbert schemes of points on the fibers of a double point degeneration. This equation resembles a computation of such Euler characteristics via a combinatorial inclusion–exclusion principle. As a consequence, we show the existence of universal polynomials for the Euler characteristics of tautological sheaves on the Hilbert scheme of points on smooth proper algebraic spaces. We apply this result to a conjecture of Zhou on tautological sheaves on Hilbert schemes of points, and reduce the conjecture to the cases of products of projective spaces. Our main tools are good degenerations and algebraic cobordism.

We prove Kuznetsov’s conjecture on the fullness of exceptional collections in the line bundles case for the blow-up of ({mathbb {P}}^{5}) along the image of Segre threefold ({mathbb {P}}^{1}times {mathbb {P}}^{2}) and its hyperplane section.

Certain Iwahori double cosets in the loop group of a reductive group, known under the names of P-alcoves or ((J,w,delta ))-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.

Petrecca and Röser (Mathematische Zeitschrift 291:395–419, 2018) and Schueth (Ann Global Anal Geom 52:187–200, 2017) had shown that for a generic G-invariant metric g on certain compact homogeneous spaces (M=G/K) (including symmetric spaces of rank 1 and some Lie groups), the spectrum of the Laplace-Beltrami operator (Delta _g) was real G-simple. The same is not true for the complex version of (Delta _g) when there is a presence of representations of complex or quaternionic type. We show that these types of representations induces a (Q_8)-action that commutes with the Laplacian in such way that G-properties of the real version of the operator have to be understood as ((Q_8 times G))-properties on its corresponding complex version.

A space X is W-trivial if for every real vector bundle (alpha ) over X the total Stiefel-Whitney class (w(alpha )) is 1. It follows from a result of Milnor that if X is an orientable closed smooth manifold of dimension 1, 2, 4 or 8, then X is not W-trivial. In this note we completely characterize W-trivial orientable connected closed smooth manifolds in dimensions 3, 5 and 6. In dimension 7, we describe necessary conditions for an orientable connected closed smooth 7-manifold to be W-trivial.

In this paper, we completely classify 3-dimensional complete self-expanders with constant squared norm S of the second fundamental form and constant (f_{3}) in the Euclidean space ({mathbb {R}}^{4}), where (h_{ij}) are components of the second fundamental form, (S=sum _{i,j}h^{2}_{ij}) and (f_{3}=sum _{i,j,k}h_{ij}h_{jk}h_{ki}).

Let F be an archimedean local field and let E be (Ftimes F) (resp. a quadratic extension of F). We prove that an irreducible generic (resp. nearly tempered) representation of (textrm{GL}_n(E)) is (textrm{GL}_n(F)) distinguished if and only if its Rankin-Selberg (resp. Asai) L-function has an exceptional pole of level zero at 0. Further, we deduce a necessary condition for the ramification of such representations using the theory of weak test vectors developed by Humphries and Jo.

We prove a finiteness theorem and a comparison theorem in the theory of étale cohomology of rigid analytic varieties. By a result of Huber, for a quasi-compact separated morphism of rigid analytic varieties with target being of dimension (le 1), the compactly supported higher direct image preserves quasi-constructibility. Though the analogous statement for morphisms with higher dimensional target fails in general, we prove that, in the algebraizable case, it holds after replacing the target with a modification. We deduce it from a known finiteness result in the theory of nearby cycles over general bases and a new comparison result, which gives an identification of the compactly supported higher direct image sheaves, up to modification of the target, in terms of nearby cycles over general bases.

In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational singularities and prove basic properties of such objects. Natural examples of singular contact varieties come from the theory of nilpotent orbits: every projectivization of the closure of a nilpotent orbit in a semisimple Lie algebra satisfies our definition after normalization. We show the correspondence between symplectic varieties with the structure of a (mathbb {C}^*)-bundle and the contact ones along with the existence of stratification à la Kaledin. In the projective case we demonstrate the equivalence between crepant and contact resolutions of singularities, show the uniruledness and give a full classification of projective contact varieties in dimension 3.