We prove that, for every $n\ge9$, no ordered GIT quotient of $n$ points on $\mathbb P^1$ with positive rational weights smaller than one and of total weight two is isomorphic to the Baily--Borel compactification of an arithmetic complex ball quotient. The weights may lie on stability walls, and the lattice may have tor...
We study the canonical formal solution space of a homogeneous $A$-hypergeometric system in a generic direction. We present as a finite-dimensional cokernel the quotient of that space by the span of the canonical series obtained by intrinsic perturbation, taken over all exponents occurring in that space and all ordered...
We consider the family of cyclic fourfold covers $w^4 = \prod_{j=1}^{7}(z-x_j)$ of the complex projective line branched at the eight points $x_1,\ldots,x_7,\infty$. The period map identifies the configuration space $X(2,8)$ of the branch points with a Zariski open subset of a quotient of the five-dimensional complex ba...
We show that, at a fake exponent of an $A$-hypergeometric system and for an ordered negative support family, intrinsic perturbation within $\ker_{\mathbb{Z}}(A)$ can produce a strictly smaller coefficient space than ambient perturbation, which answers a question of Okuyama--Saito. We measure the failure by an intrinsic...
We show that, at a fake exponent of an $A$-hypergeometric system and for an ordered negative support family, intrinsic perturbation within $\ker_{\mathbb{Z}}(A)$ can produce a strictly smaller coefficient space than ambient perturbation, which answers a question of Okuyama--Saito. We measure the gap by an intrinsic-per...
Ryunosuke Nakano· 0 citations
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