Gordon Heier
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A Schmidt–Nochka theorem for closed subschemes in subgeneral position Open
In previous work, the authors established a generalized version of Schmidt’s subspace theorem for closed subschemes in general position in terms of Seshadri constants. We extend our theorem to weighted sums involving closed subschemes in s…
On the zero set of holomorphic sectional curvature Open
A notable example due to Heier, Lu, Wong, and Zheng shows that there exist compact complex Kähler manifolds with ample canonical line bundle such that the holomorphic sectional curvature is negative semi-definite and vanishes along high-di…
On positive semi-definite holomorphic sectional curvature with many zeroes Open
We establish the existence of complete Kähler metrics of semi-positive holomorphic sectional curvature with many zeroes in an interesting and natural geometric setting. Specifically, we use Calabi's Ansatz in the form due to Koiso-Sakane t…
A Schmidt-Nochka Theorem for closed subschemes in subgeneral position Open
In previous work, the authors established a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of Seshadri constants. We extend our theorem to weighted sums involving closed subschemes in s…
A generalized Schmidt subspace theorem for closed subschemes Open
We prove a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of suitably defined Seshadri constants with respect to a fixed ample divisor. Our proof builds on previous work by Evertse and …
On Projective Kähler Manifolds of Partially Positive Curvature and Rational Connectedness Open
In a previous paper, we proved that a projective Kähler manifold of positive total scalar curvature is uniruled. At the other end of the spectrum, it is a well-known theorem of Campana and Kollár-Miyaoka-Mori that a projective Kähler manif…
On the degeneracy of integral points and entire curves in the complement\n of nef effective divisors Open
As a consequence of our recently established generalized Schmidt's subspace\ntheorem for closed subschemes in general position, we prove a degeneracy\ntheorem for integral points on the complement of a union of nef effective\ndivisors. A n…
On projectivized vector bundles and positive holomorphic sectional curvature Open
We generalize a construction of Hitchin to prove that, given any compact Kähler manifold with positive holomorphic sectional curvature and any holomorphic vector bundle over , the projectivized vector bundle admits a Kähler metric with pos…
Reduction of manifolds with semi-negative holomorphic sectional curvature Open
In this note, we continue the investigation of a projective Kähler manifold $M$ of semi-negative holomorphic sectional curvature $H$. We introduce a new differential geometric numerical rank invariant which measures the number of linearly …
Kähler manifolds of semi-negative holomorphic sectional curvature Open
In an earlier work, we investigated some consequences of the existence of a Kähler metric of negative holomorphic sectional curvature on a projective manifold. In the present work, we extend our results to the case of semi-negative (i.e., …
On projectivized vector bundles and positive holomorphic sectional curvature Open
We generalize a construction of Hitchin to prove that, given any compact Kähler manifold $M$ with positive holomorphic sectional curvature and any holomorphic vector bundle $E$ over $M$, the projectivized vector bundle ${\mathbb P}(E)$ adm…