arXiv subjects
Publications and source records attributed to Ying Zong.
Every finite flat finitely presented group scheme G of square free order over a scheme S can be written as an extension of a finite etale S-group scheme G" by a commutative finite flat finitely presented S-group scheme G' that is a direct sum of group schemes of prime order. Such an extension splits over a finite etale surjective base change.
Elliptic K3 admit contraction to plane models, the Weierstrass models. We define a higher dimensional notion of Weierstrass models, show that they are compactification of torsors in a unique form, and propose an application to the kahler geometry of a class of lagrangian fibrations on irreducible symplectic manifolds.
Let S be an algebraic space, A an S-abelian algebraic space, L an S-fiberwise numerically trivial invertible module on A, and L* the sheaf of regular sections of L considered as a G_m-torsor on A. We classify the S-minimal models of L* into two types.
The existence of an equidimensional morphism f with etale local sections from a regular algebraic space X to a locally noetherian normal algebraic space S of characteristic zero with excellent local rings implies that S is regular and f flat.
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
We provide evidence for the Principle : Non-uniruled abelian fibrations are almost non-degenerate.
We characterize quotient of a non-degenerate abelian fibration by a finite étale equivalence relation. We show that non-uniruled degenerations of each such quotient tend to be almost non-degenerate.
We partially answer, in terms of monodromy, Murty and Patankar's question: Given an absolutely simple abelian variety over a number field, does it have simple specializations at a set of places of positive Dirichlet density? The answer is based on the classification of pairs (G,V) consisting of a semi-simple algebraic group G over a non-archimedean local field and an absolutely irreducible representation V of G such that G admits a maximal torus acting irreducibly on V.