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

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.

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.

On the dualizing sheaf of a quotient scheme

1984 ◽  
Vol 12 (15) ◽  
pp. 1855-1869 ◽  
Author(s):  
Barbara R. Peskin
Keyword(s):  
Dualizing Sheaf

scholarly journals The dualizing sheaf on first-order deformations of toric surface singularities

2019 ◽  
Vol 2019 (753) ◽  
pp. 137-158 ◽  
Author(s):  
Klaus Altmann ◽  
János Kollár
Keyword(s):  
Moduli Space ◽  
General Type ◽  
Surfaces Of General Type ◽  
Toric Surface ◽  
First Order ◽  
Surface Singularities ◽  
Quotient Singularities ◽  
Infinitesimal Deformations ◽  
Cyclic Quotient Singularities ◽  
Dualizing Sheaf

AbstractWe explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár–Shepherd-Barron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.

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