Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials
TL;DR: In this article, the Masur-Veech volumes and area Siegel Veech constants were obtained using intersection theory on strata of Abelian differentials with prescribed orders of zeros.
read more
Abstract: We show that the Masur–Veech volumes and area Siegel–Veech constants can be obtained using intersection theory on strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel–Veech constants for all strata. We also show that the same results hold for the spin and hyperelliptic components of the strata.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Posted Content
Volumes of moduli spaces of flat surfaces
TL;DR: The moduli spaces of flat surfaces with prescribed conical singularities were studied in this paper, where it was shown that the volumes of these spaces are finite and that they are explicitely computable by induction on the Euler characteristics of the punctured surface.
8
•Posted Content
The area is a good metric
Matteo Costantini,Martin Möller,Jonathan Zachhuber +2 more
- 30 Oct 2019
TL;DR: In this article, the authors extend the smooth normal-crossing divisors compactification of projectivized strata of abelian differentials given by Bainbridge, Chen, Gendron, Grushevsky and Moeller to the case of k-differentials.
7
Regularized Integrals on Riemann Surfaces and Modular Forms
TL;DR: In this paper, a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces is introduced, which gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.
7
•Posted Content
The Large genus asymptotic expansion of Masur-Veech volumes
TL;DR: In this article, Chen et al. studied the asymptotic behavior of Masur-Veech volumes as the genus goes to infinity and showed the existence of a complete expansion of these volumes that depends only on the genus and the number of singularities.
6
A symmetric Bloch-Okounkov theorem
TL;DR: In this paper, a quasimodular algebra of shifted symmetric functions on partitions has been introduced, consisting of symmetric polynomials in the part sizes and multiplicities.
References
•Book
Symmetric functions and Hall polynomials
Ian G. MacDonald
- 01 Jan 1979
TL;DR: In this paper, the characters of GLn over a finite field and the Hecke ring of GLs over finite fields have been investigated and shown to be symmetric functions with two parameters.
10.4K
Geometry of algebraic curves
Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths,Joe Harris +3 more
- 01 Jan 1985
TL;DR: This chapter discusses Brill-Noether theory on a moving curve, and some applications of that theory in elementary deformation theory and in tautological classes.
2.9K
Intersection theory on the moduli space of curves and the matrix Airy function
TL;DR: In this article, it was shown that two natural approaches to quantum gravity coincide, relying on the equivalence of each approach to KdV equations, and they also investigated related mathematical problems.
Towards an Enumerative Geometry of the Moduli Space of Curves
David Mumford
- 01 Jan 1983
TL;DR: In this paper, a Chow ring for the moduli space M g of curves of genus g and its compactification M g is defined, defining what seem to be the most important classes in this ring and calculating the class of some geometrically important loci in M g in terns of these classes.
•Book
Moduli of curves
Joe Harris,Ian Morrison +1 more
- 01 Jan 1998
TL;DR: In this article, the Brill-Noether theory is applied to moduli spaces of curves of curves, and a technique for construction of M_g is described, based on the limit linear series and the Brill noether theory.