2 citations · 2 across the 7 of their papers we have counts for
7 papers
Remarks on the sections of universal hyperelliptic curves
Tatsunari Watanabe
In this paper, we study the obstruction for the sections of the universal hyperelliptic curves of genus . The obstruction of our interest comes from the relative completio…
Non-abelian cohomology of universal curves in positive characteristic
Tatsunari Watanabe
In this paper, we will compute the non-abelian cohomology of the universal complete curve in positive characteristic. This extends Hain's result on the non-abelian cohomology of ge…
Remarks on Collino cycles and hyperelliptic Johnson homomorphisms
Ma Luo, Tatsunari Watanabe
A Collino cycle is a higher cycle on the Jacobian of a hyperelliptic curve. The universal family of Collino cycles naturally gives rise to a normal function, whose induced monodrom…
Remarks on Rational Points of Universal Curves
Tatsunari Watanabe
In this notes, we will give some remarks on the results in Rational points of universal curves by Hain. In particular, we consider the universal curves $\mathcal{M}_{g,n+1}\to \mat…
On the completion of the mapping class group of genus two
Tatsunari Watanabe
In this paper, we will study the Lie algebra of the prounipotent radical of the relative completion of the mapping class group of genus two. In particular, we will partially determ…
On the sections of universal hyperelliptic curves
Tatsunari Watanabe
In this paper, we will give an algebraic proof for determining the sections for the universal pointed hyperelliptic curves, when and the image of the -adic cyclotom…
Rational points of universal curves in positive characteristics
Tatsunari Watanabe
For the moduli stack of smooth curves over with the function field , we show that if , then the only -rati…