Gordon Heier
Research interests:
Algebraic Geometry, Complex Analysis, Differential Geometry, and Number Theory.
List of Research Keywords:
Effective methods in algebraic geometry, complex analysis, and number theory, multiplier ideal sheaves, vanishing theorems, positivity, Fujita Conjecture, Shafarevich Conjecture, Mordell Conjecture, integral and rational points, Schmidt subspace theorem, hyperbolicity, effective Nullstellensatz, finite type domains, complex Neumann problem, Kähler-Einstein metrics and Kähler-Ricci flow on Fano manifolds, (weakly) negative/positive curvature in complex differential geometry, holomorphic sectional curvature, (total) scalar curvature, uniruledness, rational connectedness.
Grant Support:
- Simons Foundation, Collaboration Grant for Mathematicians, 2022-2027
- National Security Agency, Grant Number H98230-12-1-0235, 2012-2014
Publications and Preprints:
- G. Heier, A. Levin. A Schmidt-Nochka Theorem for closed subschemes in subgeneral position. J. Reine Angew. Math., in press. (arXiv:2308.11460)
- M. Chen, G. Heier. On positive semi-definite holomorphic sectional curvature with many zeroes. Comm. Anal. Geom., in press. (arXiv:2308.12555)
- Y. Chen, G. Heier. On the zero set of holomorphic sectional curvature. Math. Nachr., 297:2333--2352, 2024.
- G. Heier, A. Levin. A generalized Schmidt subspace theorem for closed subschemes. Amer. J. Math., 143(1):213--226, 2021.
- G. Heier, A. Levin. On the degeneracy of integral points and entire curves in the complement of nef effective divisors. J. Number Theory, 217:301--319, 2020.
- G. Heier, B. Wong. On projective Kähler manifolds of partially positive curvature and rational connectedness. Doc. Math., 25:219--238, 2020.
- A. Chaturvedi, G. Heier. Hermitian metrics of positive holomorphic sectional curvature on fibrations. Math. Z., 295:349--364, 2020.
- G. Heier, S. S. Y. Lu, B. Wong, F. Zheng. Reduction of manifolds with semi-negative holomorphic sectional curvature. Math. Ann., 372:951--962, 2018.
- A. Alvarez, G. Heier, F. Zheng. On projectivized vector bundles and positive holomorphic sectional curvature. Proc. Amer. Math. Soc., 146(7):2877--2882, 2018.
- G. Heier, S. Takayama. Effective degree bounds for generalized Gauss map images. Adv. Stud. Pure Math., 74:203--236, 2017.
- G. Heier, S. S. Y. Lu, B. Wong. Kähler manifolds of semi-negative holomorphic sectional curvature. J. Differential Geom., 104(3):419--441, 2016.
- A. Alvarez, A. Chaturvedi, G. Heier. Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces. Contemp. Math., 654:133--142, 2015.
- G. Heier. Uniformly effective boundedness of Shafarevich Conjecture-type. J. Reine Angew. Math., 674:99--111, 2013.
- G. Heier, B. Wong. Scalar curvature and uniruledness on projective manifolds. Comm. Anal. Geom., 20(4):751--764, 2012.
- G. Heier, M. Ru. On essentially large divisors. Asian J. Math., 16(3):387--408, 2012.
- G. Heier, S. Takayama. On uniformly effective birationality and the Shafarevich Conjecture over curves. arXiv:1105.3439.
- G. Heier, S. S. Y. Lu, B. Wong. On the canonical line bundle and negative holomorphic sectional curvature. Math. Res. Lett., 17(6):1101--1110, 2010.
- G. Heier. Existence of Kähler-Einstein metrics and multiplier ideal sheaves on del Pezzo surfaces. Math. Z., 264(4):727--743, 2010.
- G. Heier. Convergence of the Kähler-Ricci flow and multiplier ideal sheaves on del Pezzo surfaces. Michigan Math. J., 58(2):423--440, 2009.
- G. Heier. Finite type and the effective Nullstellensatz. Comm. Algebra, 6(8):2947--2957, 2008.
- G. Heier. Effective finiteness theorems for maps between canonically polarized compact complex manifolds. Math. Nachr., 278(1-2):133--140, 2005.
- G. Heier. Uniformly effective Shafarevich Conjecture on families of
hyperbolic curves over a curve with prescribed degeneracy locus. J. Math. Pures Appl. (9), 83(7):845--867, 2004.
- G. Heier. Effective freeness of adjoint line bundles. Doc. Math., 7:31--42, 2002.