6 papers · 1 filter
Three vignettes on hypergeometric normal functions
Matt Kerr
We use Hodge-theoretic methods to (i) explain number-theoretic identities of a type recently considered by Guillera and Zudilin, (ii) describe the Frobenius dual of Abel-Jacobi per…
Hodge adjacency conditions for singularities
RJ Acuna, Matt Kerr
We prove compatibility relations between mixed Hodge numbers of -Du Bois fibers in flat projective families and versal deformations of isolated -Du Bois singularities. These…
The arithmetic of Calabi-Yau motives and mobile higher regulators
Vasily Golyshev, Matt Kerr
We construct elements in the motivic cohomology of certain rank 4 weight 3 Calabi--Yau motives, and write down explicit expressions for the regulators of these elements in the cont…
Non-vanishing of Ceresa and Gross--Kudla--Schoen cycles associated to modular curves
Matt Kerr, Wanlin Li, Congling Qiu +1
Associated to an algebraic curve , there are two canonically constructed homologically trivial algebraic -cycles, the Ceresa cycle in the Jacobian of , and the Gross-Kudla…
Real regulator maps with finite 0-locus
RJ Acuna, Devin Akman, Matt Kerr
A Laurent polynomial in two variables is tempered if its edge polynomials are cyclotomic. Variation of coefficients leads to a family of smooth complete genus curves carrying a…
On the torsion locus of the Ceresa normal function
Matt Kerr, Salim Tayou
We prove that the positive-dimensional part of the torsion locus of the Ceresa normal function in is not Zariski dense when . Moreover, it has only finitel…