scholarly journals Self-intersection of the relative dualizing sheaf on modular curves X_1(N)

2014 ◽  
Vol 26 (1) ◽  
pp. 111-161 ◽  
Author(s):  
Hartwig Mayer
Keyword(s):  
Modular Curves ◽  
Dualizing Sheaf

scholarly journals On the genus of some modular curves of level N

1996 ◽  
Vol 54 (2) ◽  
pp. 291-297 ◽  
Author(s):  
Chang Heon Kim ◽  
Ja Kyung Koo
Keyword(s):  
Modular Curves

We estimate the genus of the modular curves X1(N).

scholarly journals Faltings modular height and self-intersection of dualizing sheaf

1995 ◽  
Vol 220 (1) ◽  
pp. 273-278
Author(s):  
Atsushi Moriwaki
Keyword(s):  
Dualizing Sheaf

Zeta functions of twisted modular curves

2006 ◽  
Vol 80 (1) ◽  
pp. 89-103 ◽  
Author(s):  
Cristian Virdol
Keyword(s):  
Zeta Function ◽  
Galois Group ◽  
Complex Plane ◽  
Zeta Functions ◽  
Modular Curves ◽  
Absolute Galois Group ◽  
Modular Curve ◽  
The Absolute

AbstractIn this paper we compute and continue meromorphically to the whole complex plane the zeta function for twisted modular curves. The twist of the modular curve is done by a modprepresentation of the absolute Galois group.

scholarly journals Normal functions and the height of Gross-Schoen cycles

2014 ◽  
Vol 214 ◽  
pp. 53-77 ◽  
Author(s):  
Robin De Jong
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
The Self ◽  
Compact Type ◽  
Stable Curves ◽  
Normal Functions ◽  
Chern Form ◽  
Bloch Line ◽  
Pointed Curve ◽  
Dualizing Sheaf

AbstractWe prove a variant of a formula due to Zhang relating the Beilinson– Bloch height of the Gross–Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach, the height of the Gross–Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is nonnegative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal Jacobian.

Sign in / Sign up

Export Citation Format

Share Document