A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Classifies connected components of meromorphic differentials with residue conditions.
This paper classifies components of meromorphic differential strata.
Study classifies Morse functions with 4 critical points on immersed 2-spheres.
Alternative proof for non-existence of complete curves in differential strata.
Classifies components of strata of k-differentials on Riemann surfaces.
The paper studies components of abelian differentials on surfaces, finding multiple components not seen in unmarked surfaces.
In this paper, we study connected components of strata of the space of quadratic differentials lying over $\T_g$. We use certain general properties of sections of line bundles to put a upper bound on the number of connected components, and a generalized version of the Gauss map as an invariant to put a lower bound on t…
Harmonic maps to Euclidean buildings have rectifiable singular strata.
Configurations of rigid collections of saddle connections are connected component invariants for strata of the moduli space of quadratic differentials. They have been classified for strata of Abelian differentials by Eskin, Masur and Zorich. Similar work for strata of quadratic differentials has been done in Masur and …
In two fundamental classical papers, Masur and Veech have independently proved that the Teichmueller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved…
The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials. This allows us to compute the Kodaira dimension of some strata of the moduli space of Abelian differentials. The main ingredients to study the compactifications of the strata ar…
Study calculates volumes and constants from intersection theory on abelian differential strata.
Moduli spaces of Abelian and quadratic differentials are stratified by multiplicities of zeroes; connected components of the strata correspond to ergodic components of the Teichmuller geodesic flow. It is known that the strata are not necessarily connected; the connected components were recently classified by M. Kontse…
Very few results are known about the topology of the strata of the moduli space of quadratic differentials. In this paper, we prove that any connected component of such strata has only one topological end. A typical flat surface in a neighborhood of the boundary is naturally split by a collection of parallel short sadd…
Connected boundaries of strata of differentials are always connected in various compactifications.
Non-asphericity of strata of genus-one differentials
In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that contain regular fundamental strata with fixed combinatorics at each singular point …
Translation surfaces with poles correspond to meromorphic differentials on compact Riemann surfaces. They appear in compactifications of strata of the moduli space of Abelian differentials and in the study of stability conditions. Such structures have different geometrical and dynamical properties than usual translatio…
In this paper, we study the translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces. We compute the number of connected components of the corresponding strata of the moduli space. We show that in genus greater than or equal to two, one has up to three components with a similar descri…
Study of quasi-Kähler metrics on complex manifolds linked to c-projective metrizability.
The study characterizes a complex curve of residueless meromorphic differentials on elliptic curves.
Estimates surface count with prescribed foliations.
The paper counts ends of differential forms on surfaces.
Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian differentials. The open strata can have up to three connected c…
We establish a connection between Morin singularities and stable homotopy groups of spheres. This connection allows us to describe how the images of singularity strata behave around the image of a more complicated stratum.
This paper studies connectivity of cyclic-Schottky strata in Schottky space.
Study shows monodromy kernels are large, failing to prove commensurability in specific strata.
The paper calculates large genus limits for two types of Siegel-Veech constants.
The object of this paper is to study GL(2,R) orbit closures in hyperelliptic components of strata of abelian differentials. The main result is that all higher rank affine invariant submanifolds in hyperelliptic components are branched covering constructions, i.e. every translation surface in the affine invariant subman…
Pseudo-Riemannian metrics with Levi-Civita connection in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the maximal rank solutions of a certain overdetermined projectively invariant differential equation often called the metrizability equation. Dropping this …
Generalizes results for lambda-connections and Higgs bundles.
Moduli spaces of quadratic differentials with prescribed singularities are not necessarily connected. We describe here all cases when they have a special hyperelliptic connected component. We announce the general classification theorem: up to the four exceptional cases in low genera the strata of meromorphic quadratic …
Classifies components of abelian differentials over Teichmüller space.
The paper decomposes spectral functions on marked tori strata.
Solves Deligne-Simpson problem for special connections on Gm.
Classifies orbit closures in translation surface strata.
Formula for volumes of odd strata of quadratic differentials using graph intersection numbers.
Constructs a function to prove meromorphic differential strata don't have complete subvarieties.
The paper proves properties of strata of differentials, showing they are affine and extremal.
This paper is devoted to the classification of connected components of Prym eigenform loci in the strata H(2,2)^odd and H(1,1,2) in the Abelian differentials bundle in genus 3. These loci, discovered by McMullen are GL^+(2,R)-invariant submanifolds (of complex dimension 3) that project to the locus of Riemann surfaces …
The paper constructs cohomology classes on curve strata.
We extend asymptotic formulas for saddle connections on translation surfaces.
The paper studies tautological rings of strata of differentials, proving cohomological stability and no relations in specific degrees.
Homology of abelian differentials stabilizes with more zeros.
Survey of compactifications for differential strata.
Let X be a Hermitian locally symmetric space. We prove that every Chern class of X has a canonical lift to the cohomology of the Baily- Borel-Satake compactification X* of X and that the resulting Chern numbers satisfy the Hirzebruch proportionality formula with respect to the compact dual X^ of X. The same result hold…
Study the boundary of Riemann surfaces with abelian automorphisms.
We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.