For abelian varieties of dimension at most three, higher Chow cycles yield meromorphic Siegel modular forms of weight Sym^4 det^-1, and the K-theory elevator matches the Siegel operator under rank-one degeneration.
Siegel operators for holomorphic differential forms
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We give a geometric interpretation of the Siegel operators for holomorphic differential forms on Siegel modular varieties. This involves extension of the differential forms over a toroidal compactification, and we show that the Siegel operator essentially describes the restriction and descent to the boundary Kuga variety via holomorphic Leray filtration. As a consequence, we obtain equivalence of various notions of "vanishing at boundary'' for holomorphic forms. We also study the case of orthogonal modular varieties.
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Siegel modular forms arising from higher Chow cycles
For abelian varieties of dimension at most three, higher Chow cycles yield meromorphic Siegel modular forms of weight Sym^4 det^-1, and the K-theory elevator matches the Siegel operator under rank-one degeneration.