Defect relations of holomorphic curves and their associated curves in CPm

1979 ◽  
pp. 398-404
Author(s):  
Chen-Han Sung
Keyword(s):  
Holomorphic Curves

scholarly journals The Adjunction Inequality for Weyl-Harmonic Maps

2020 ◽  
Vol 7 (1) ◽  
pp. 129-140
Author(s):  
Robert Ream
Keyword(s):  
Minimal Surfaces ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Weyl Connection ◽  
Almost Kähler ◽  
Conformal Manifolds

AbstractIn this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality\chi \left( {{T_f}\sum } \right) + \chi \left( {{N_f}\sum } \right) \le \pm {c_1}\left( {f*{T^{\left( {1,0} \right)}}M} \right).The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well as their extension to almost-Kähler 4-manifolds by Chen-Tian, Ville, and Ma.

scholarly journals Holomorphic curves in Shimura varieties

2018 ◽  
Vol 111 (4) ◽  
pp. 379-388 ◽  
Author(s):  
Michele Giacomini
Keyword(s):  
Abelian Varieties ◽  
Holomorphic Curves ◽  
Zariski Closure ◽  
Shimura Varieties

Abstract We prove a hyperbolic analogue of the Bloch–Ochiai theorem about the Zariski closure of holomorphic curves in abelian varieties. We consider the case of non compact Shimura varieties completing the proof of the result for all Shimura varieties. The statement which we consider here was first formulated and proven by Ullmo and Yafaev for compact Shimura varieties.

Sign in / Sign up

Export Citation Format

Share Document