Related papers: An arithmetic Yau-Zaslow formula
We associate weight complexes of (homological) motives, and hence Euler characteristics in the Grothendieck group of motives, to arithmetic varieties and Deligne-Mumford stacks; this extends the results in the paper "Descent, Motives and…
We prove a generalization of the Li-Yau estimate for a board class of second order linear parabolic equations. As a consequence, we obtain a new Cheeger-Yau inequality and a new Harnack inequality for these equations. We also prove a…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
We compute the Suslin homology of relative curves with modulus. This result may be regarded as a modulus version of the computation of motives for curves, due to Suslin and Voevodsky.
Salikhov has proved a conjecture of Kontsevich and Shoikhet by reducing it to the consideration of three families of graphs, a consideration which was left to the reader for two of those families. We show, that the conjecture is just a very…
We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi…
We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized abelian threefolds together with a level…
Here we review background in differential topology related to the calculation of an euler characteristic, and background on localization in equivariant cohomology. We then outline Gromov-Witten invariants in algebraic geometry and give…
We prove Li-Yau-Kr\"oger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a…
By resolving an arbitrary perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in the 4-dimensional projective space. These numbers…
We prove a Liouville type theorem for entire maximal $m$-subharmonic functions in $\mathbb C^n$ with bounded gradient. This result, coupled with a standard blow-up argument, yields a (non-explicit) a priori gradient estimate for the complex…
Haken n-manifolds have been defined and studied by B. Foozwell and H. Rubinstein in analogy with the classical Haken manifolds of dimension 3, based upon the the theory of boundary patterns developed by K. Johannson. The Euler…
We present a detailed proof of Wolstenholme's theorem using an Egorychev-type contour integral and an exponential change of variables. All formal series manipulations are justified, and the connection with harmonic sums and Bernoulli…
Given a general plane curve Y of degree d, we compute the number n_d of irreducible plane conics that are 5-fold tangent to Y. This problem has been studied before by Vainsencher using classical methods, but it could not be solved there…
Flajolet and Salvy pointed out that every Euler sum is a $\mathbb{Q}$-linear combination of multiple zeta values. However, in the literature, there is no formula completely revealing this relation. In this paper, using permutations and…
The main new result is the computation of the degeneration of l-adic Eisenstein classes at the cusps. This is done by relating it to the degeneration of the elliptic polylog. These classes come from K-theory and their Hodge regulator can…
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne) for the relation between the two natural products on the space of Chinese characters. The…
By the work of J.Huh, one can interpret binomial coefficients as a solution to an intersection problem on a permutohedral variety $X_E$. Applying Hirzebruch-Riemann-Roch, this intersection problem is equivalent to computing Euler…
K-theoretic Donaldson invariants are holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 sheaves on surfaces. We develop an algorithm which determines the generating functions of K-theoretic Donaldson…
An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the…