Related papers: Divisorial strata of abelian differentials

We compute the degree of Hurwitz-Hodge classes $\lambda_1^e$ on one dimensional moduli spaces of cyclic admissible covers of the projective line. We also compute the degree of the the first Chern class of the Hodge bundle $\lambda_1$ for…

We develop a $GL_{qp}(2)$ invariant differential calculus on a two-dimensional noncommutative quantum space. Here the co-ordinate space for the exterior quantum plane is spanned by the differentials that are commutative (bosonic) in nature.

In this note we investigate the connection between polylogarithms on curves and abelian schemes. The main result shows that the polylogarithm on the abelian scheme can be obtained as the push-forward of the polylogarithm on a suitable…

An abelian variety admits only a finite number of isomorphism classes of principal polarizations. The paper gives an interpretation of this number in terms of class numbers of definite Hermitian forms in the case of a product of elliptic…

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a…

Given an Edwards curve, we determine a basis for the Riemann-Roch space of any divisor whose support does not contain any of the two singular points. This basis allows us to compute a generating matrix for an algebraic-geometric Goppa code…

Given a Galois cover of curves $f$ over a field of characteristic $p$, the lifting problem asks whether there exists a Galois cover over a complete mixed characteristic discrete valuation ring whose reduction is $f$. In this paper, we…

For a finite abelian group $G$, we compute the $G$-equivariant formal group law corresponding to the $G$-equivariant complex cobordism spectrum with its canonical complex orientation.

We prove that the moduli space $\mathcal{M}_g$ of smooth curves of genus $g$ is the union of $g-1$ affine open subsets for every $g$ with $2 \le g \le 5$, as predicted by an intriguing conjecture of Eduard Looijenga.

We study the dimension of loci of special line bundles on stable curves and for a fixed semistable multidegree. In case of total degree $d = g - 1$, we characterize when the effective locus gives a Theta divisor. In case of degree $g - 2$…

Consider the moduli space of pairs (C,w) where C is a smooth compact complex curve of a given genus and w is a holomorphic 1-form on C with a given list of multiplicities of zeroes. We describe connected components of this space. This…

We compute the classes of universal theta divisors of degrees zero and g-1 over the Deligne-Mumford compactification of the moduli space of curves, with various integer weights on the points, in particular reproving a recent result of…

In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol…

Let the bielliptic locus be the closure in the moduli space of stable curves of the locus of smooth curves that are double covers of genus 1 curves. In this paper we compute the class of the bielliptic locus in \bar{M}_3 in terms of a…

We study geometric properties of linear strata of uni-singular curves. The singularities of closures of the strata are resolved and the resolutions are represent as projective bundles. This enables to study their geometry. In particular we…

Let $C$ be an affine curve over an algebraically closed field $k$ of characteristic $p>0$. Given an embedding problem $(\beta:\Gamma\longrightarrow G, \alpha: \pi^{et}_1(C)\longrightarrow G)$ for $\pi_1^{et}(C)$ where $\beta$ is a…

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…

We show (under some hypothesis in small dimensions) that the analytic degree of the divisor of a modular form on the orthogonal group O(2,p) is determined by its weight. Moreover, we prove that certain integrals, occurring in Arakelov…

Topological properties of the jacobian curve ${\mathcal J}_{\mathcal{F},\mathcal{G}}$ of two foliations $\mathcal{F}$ and $\mathcal{G}$ are described in terms of invariants associated to the foliations. The main result gives a decomposition…

We study the cone of moving divisors on the moduli space ${\mathcal A}_g$ of principally polarized abelian varieties. Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that…