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We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles.
“Obstructions to the smoothing of piecewise-differentiable homeomorphisms”
J. Munkres · 1960
Earlier work this paper cites.
“Algebraic approximation of structures over complete local rings”
M. Artin · 1969
Earlier work this paper cites.
“The irreducibility of the space of curves of given genus”
P. Deligne and D. Mumford · 1969
Earlier work this paper cites.
“Topology on spaces of holomorphic mappings”, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 47
L. Nachbin · 1969
Earlier work this paper cites.
“Quasiconformal mappings in the plane. Translated from the German by K. W. Lucas. 2nd ed.”
O. Lehto and K. Virtanen · 1973
Earlier work this paper cites.
“Spaces of degenerating Riemann surfaces”
L. Bers · 1974
Earlier work this paper cites.
“Spaces of degenerating Riemann surfaces”
L. Bers · 1974
Earlier work this paper cites.
“Degenerating families of Riemann surfaces”
W. Abikoff · 1977
Earlier work this paper cites.
“Algebraic geometry” Graduate Texts in Mathematics, No. 52
R. Hartshorne · 1977
Earlier work this paper cites.
“Geometric topology in dimensions 2 2 and 3 3 ”, Graduate Texts in Mathematics, Vol. 47
E. Moise · 1977
Earlier work this paper cites.
“Quadratic differentials and foliations”
J. Hubbard and H. Masur · 1979
Earlier work this paper cites.
“Lectures on equations defining space curves” Notes by N. Mohan Kumar
L. Szpiro · 1979
Earlier work this paper cites.
“Finite-dimensional Teichmüller spaces and generalizations”
L. Bers · 1981
Earlier work this paper cites.
“Complete intersections in Stein manifolds”
C. Banica and O. Forster · 1982
Earlier work this paper cites.
“Quadratic differentials” 5
K. Strebel · 1984
Earlier work this paper cites.
“Geometry of algebraic curves. Vol. I” 267
E. Arbarello, M. Cornalba, P.. Griffiths and J. Harris · 1985
Earlier work this paper cites.
“Complex analysis in Banach spaces. Holomorphic functions and domains of holomorphy in finite and infinite dimensions.” 120
J. Mujica · 1986
Earlier work this paper cites.
“The Teichmüller geodesic flow.”
W. Veech · 1986
Earlier work this paper cites.
“Geometric complex coordinates for Teichmüller space”
A. Marden · 1987
Earlier work this paper cites.
“Amenability, Poincaré series and quasiconformal maps”
C. McMullen · 1989
Earlier work this paper cites.
“Introduction to holomorphic functions of several variables. Vol. I” Function theory, The Wadsworth & Brooks/Cole Mathematics Series
R. Gunning · 1990
Earlier work this paper cites.
“The hyperbolic metric and the geometry of the universal curve”
S. Wolpert · 1990
Earlier work this paper cites.
“Boundary behaviour of conformal maps” 299
C. Pommerenke · 1992
Earlier work this paper cites.
“Complex dynamics and renormalization” 135
C. McMullen · 1994
Earlier work this paper cites.
“Birational geometry of algebraic varieties” With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original 134
J. Koll“’ar and S. Mori · 1998
Earlier work this paper cites.
“Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over 𝐂 {\bf C} ”
K. Kato and C. Nakayama · 1999
Cited alongside, same era.
“K-theory and cohomology of algebraic stacks: Riemann-Roch theorems, D-modules and GAGA theorems”, (1999)
B. To“”en · 1999
Cited alongside, same era.
Elsevier/North-Holland, Amsterdam, 2000, pp. xx+878
“Handbook of algebra. Vol. 2” 2 · 2000
Cited alongside, same era.
“Log smooth deformation and moduli of log smooth curves”
F. Kato · 2000
Cited alongside, same era.
“Convergence structures and applications to functional analysis”
R. Beattie and H.-P. Butzmann · 2002
Cited alongside, same era.
“Orbifold Gromov-Witten theory”
W. Chen and Y. Ruan · 2002
Cited alongside, same era.
“Uniruledness of strata of holomorphic differentials in small genus”
I. Barros · 2018
Later among the works it cites.
“Compactification of strata of Abelian differentials”
M. Bainbridge et al · 2018
Later among the works it cites.
“The algebraic hull of the Kontsevich-Zorich cocycle.”
A. Eskin, S. Filip and A. Wright · 2018
Later among the works it cites.
“Invariant and stationary measures for the SL ( 2 , ℝ ) {\rm SL}(2,\mathbb{R}) action on moduli space”
A. Eskin and M. Mirzakhani · 2018
Later among the works it cites.
“The moduli space of twisted canonical divisors”
G. Farkas and R. Pandharipande · 2018
Later among the works it cites.
“The Deligne-Mumford and the incidence variety compactifications of the strata of Ω M g \Omega M_{g} ”
Q. Gendron · 2018
Later among the works it cites.
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“Volumes of moduli spaces of flat surfaces”, (2020)
A. Sauvaget · 2004
Cited alongside, same era.
“Compactifications of symmetric and locally symmetric spaces”, Mathematics: Theory & Applications
A. Borel and L. Ji · 2006
Cited alongside, same era.
“Teichmüller theory and applications to geometry, topology, and dynamics. Vol. 1”
J. Hubbard · 2006
Cited alongside, same era.
“Euler characteristics of Teichmüller curves in genus two”
M. Bainbridge · 2007
Cited alongside, same era.
“Thick-thin decomposition for quadratic differentials”
K. Rafi · 2007
Cited alongside, same era.
“A criterion of convergence in the augmented Teichmüller space”
G. Mondello · 2009
Cited alongside, same era.
“Extending the double ramification cycle using Jacobians”
D. Holmes, J. Kass and N. Pagani · 2018
Later among the works it cites.
“Volumes and Siegel–Veech constants of ℋ \mathcal{H} ( 2 g − 2 ) (2{g}-2) and Hodge integrals”
A. Sauvaget · 2018
Later among the works it cites.
“ The Stacks project ”, 2018
The Stacks project authors · 2018
Later among the works it cites.
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M. Bainbridge et al · 2019
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