TY - JOUR

T1 - The double ramification cycle and the theta divisor

AU - Grushevsky, Samuel

AU - Zakharov, Dmitry

N1 - Publisher Copyright:
© 2014 American Mathematical Society.

PY - 2014

Y1 - 2014

N2 - We compute the classes of universal theta divisors of degrees zero and g−1 over the Deligne-Mumford compactification Mg,n of the moduli space of curves, with various integer weights on the points, in particular reproving a recent result of Müller. We also obtain a formula for the class in CHg (Mctg,n) (moduli of stable curves of compact type) of the double ramification cycle, given by the condition that a fixed linear combination of the marked points is a principal divisor, reproving a recent result of Hain. Our approach for computing the theta divisor is more direct, via test curves and the geometry of the theta divisor, and works easily over all of Mg,n. We used our extended result in another paper to study the partial compactification of the double ramification cycle.

AB - We compute the classes of universal theta divisors of degrees zero and g−1 over the Deligne-Mumford compactification Mg,n of the moduli space of curves, with various integer weights on the points, in particular reproving a recent result of Müller. We also obtain a formula for the class in CHg (Mctg,n) (moduli of stable curves of compact type) of the double ramification cycle, given by the condition that a fixed linear combination of the marked points is a principal divisor, reproving a recent result of Hain. Our approach for computing the theta divisor is more direct, via test curves and the geometry of the theta divisor, and works easily over all of Mg,n. We used our extended result in another paper to study the partial compactification of the double ramification cycle.

UR - http://www.scopus.com/inward/record.url?scp=84923046425&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2014-12153-8

DO - 10.1090/S0002-9939-2014-12153-8

M3 - Article

AN - SCOPUS:84923046425

SN - 0002-9939

VL - 142

SP - 4053

EP - 4064

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -