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\title[Masur-Veech volumes and intersection theory]
      {Masur-Veech volumes and intersection theory
        on moduli spaces of Abelian differentials}

      
\begin{document}
\author{Dawei Chen}
\thanks{Research of the first author is partially supported by the NSF CAREER grant DMS-1350396 and a von Neumann Fellowship at IAS in Spring 2019.}
\address{Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA}
\email{dawei.chen@bc.edu}

\author{Martin M\"oller}
\thanks{Research of the second author is partially supported  
  by the DFG-project MO 1884/1-1 and by the LOEWE-Schwerpunkt
``Uniformisierte Strukturen in Arithmetik und Geometrie''.}
\address{
Institut f\"ur Mathematik, Goethe--Universit\"at Frankfurt,
Robert-Mayer-Str. 6--8,
60325 Frankfurt am Main, Germany
}
\email{moeller@math.uni-frankfurt.de}

\author{Adrien Sauvaget}
\thanks{Research of the third author is partially supported by the Dutch Research Council (NWO) grant 613.001.651.}
\address{Universit\'e de Cergy-Pontoise, Laboratoire de Math\'ematiques AGM, UMR 8088 du CNRS, 2 av. Adolphe
Chauvin 95302 Cergy-Pontoise Cedex, France}
\email{a.c.b.sauvaget@uu.nl, adrien.sauvaget1@u-cergy.fr}

\author{Don Zagier}
\address{MPIM Bonn, Vivatsgasse 7,
  53111 Bonn, Germany
}
\email{donzagier@mpim-bonn.mpg.de}


\maketitle

\begin{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.  
\end{abstract}

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