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.
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.
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.
AbstractWe generalize Bondal and Orlov's Reconstruction Theorem for a Gorenstein schemeXand a projective morphismX→Twhose (relative) dualizing sheaf is eitherT-ample orT-antiample.
The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf