arXiv subjects

Jingyue Chen

Publications and source records attributed to Jingyue Chen.

3 recordsLinked to original sources

arXiv2018

Differential zeros of period integrals and generalized hypergeometric functions

In this paper, we study the zero loci of local systems of the form $δΠ$, where $Π$ is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space $X$, and $δ$ is a given differential operator on the space of sections $V^\vee=Γ(X,K_X^{-1})$. Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of $δΠ$. As applications, we prove that the locus is algebraic and in some cases, non-empty. We also give an explicit way to compute the polynomial defining equations of the locus in some cases. This description gives rise to a natural stratification to the zero locus.

math.AG↗

arXiv2017

Holonomic Systems for Period Mappings

Period mappings were introduced in the sixties [G] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently [LSY,LY] to understand period integrals of algebraic manifolds. In this paper, we give an explicit construction of a tautological system for each component of a period mapping.

math.AG↗

arXiv2016

CY Principal Bundles over Compact Kähler Manifolds

A CY bundle on a connected compact complex manifold $X$ was a crucial ingredient in constructing differential systems for period integrals in [LY], by lifting line bundles from the base $X$ to the total space. A question was therefore raised as to whether there exists such a bundle that supports the liftings of all line bundles from $X$, simultaneously. This was a key step for giving a uniform construction of differential systems for arbitrary complete intersections in $X$. In this paper, we answer the existence question in the affirmative if $X$ is assumed to be Kähler, and also in general if the Picard group of $X$ is assumed to be discrete. Furthermore, we prove a rigidity property of CY bundles if the principal group is an algebraic torus, showing that such a CY bundle is essentially determined by its character map.

math.AG↗