712 research outputs found
The ring of differential Fourier expansions
For a fixed prime we prove structure theorems for the kernel and the image of
the map that attaches to any differential modular function its differential
Fourier expansion. The image of this map, which is the ring of differential
Fourier expansions, plays the role of ring of functions on a "differential
Igusa curve". Our constructions are then used to perform an analytic
continuation between isogeny covariant differential modular forms on the
differential Igusa curves belonging to different primes
On motivic principal value integrals
Inspired by p-adic (and real) principal value integrals, we introduce motivic
principal value integrals associated to multi-valued rational differential
forms on smooth algebraic varieties. We investigate the natural question
whether (for complete varieties) this notion is a birational invariant. The
answer seems to be related to the dichotomy of the Minimal Model Program.Comment: 14 page
Siegel modular forms of genus 2 and level 2
We study vector-valued Siegel modular forms of genus 2 and level 2. We
describe the structure of certain modules of vector-valued modular forms over
rings of scalar-valued modular forms.Comment: 46 pages. To appear in International Journal of Mathematic
Graph cohomology and Kontsevich cycles
The dual Kontsevich cycles in the double dual of associative graph homology
correspond to polynomials in the Miller-Morita-Mumford classes in the integral
cohomology of mapping class groups. I explain how the coefficients of these
polynomials can be computed using Stasheff polyhedra and results from my
previous paper GT/0207042.Comment: 36 pages, 3 figure
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