[CZ08] P. Corvaja and U. Zannier, 'Some cases of Vojta's Conjecture on integral points over function fields', *J. Algebraic Geometry* **17** (2008), 195-333.

[CZ10] P. Corvaja and U. Zannier, 'Integral points, divisibility between values of polynomials and entire curves on surfaces', *Adv. Math.* **225**(2) (2010), 1095-1118.

[CZ13] P. Corvaja and U. Zannier, 'Algebraic hyperbolicity of ramified covers of $G_m^2$ (and integral points on affine subsets of $\mathbb{P}_2$)', *J. Differential Geom.* **93**(3) (2013), 355-377.

[Dem97] J.-P. Demailly, 'Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials', in *Algebraic geometry—Santa Cruz 1995, Proceedings of Symposia in Pure Mathematics*, 62, (American Mathematical Society, Providence, RI, 1997), 285-360.

[Fal94] G. Faltings, 'The general case of S. Lang’s conjecture', in *Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), Perspectives in Mathematics*, 15 (Academic Press, San Diego, 1994), 175-182.

[FM94] R. Friedman and J. W. Morgan, *Smooth Four-Manifolds and Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3)*, 27 (Springer-Verlag, Berlin, 1994).

[Gra65] H. Grauert, 'Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper', *Publ. Math. Inst. Hautes Études Sci.* **25** (1965), 131-149.

[GW19] J. Guo and J. T.-Y. Wang, 'Asymptotic gcd and divisible sequences for entire functions', *Trans. Amer. Math. Soc.* **371**(9) (2019), 6241-6256.

[HR18] S. Hussein and M. Ru, 'A general defect relation and height inequality for divisors in subgeneral position', *Asian J. Math.* **22**(3) (2018), 477-491.

[HS00] M. Hindry and J. H. Silverman, *Diophantine Geometry*, Graduate Texts in Mathematics, 201 (Springer-Verlag, New York, 2000). *An introduction*.

[HT00] J. Harris and Y. Tschinkel, 'Rational points on quartics', *Duke Math. J.* **104**(3) (2000), 477-500.

[HT01] B. Hassett and Y. Tschinkel, 'Density of integral points on algebraic varieties', in *Rational Points on Algebraic Varieties*, Progress in Mathematics, 199, (Birkhäuser, Basel, 2001), 169-197.

[JX20] A. Javanpeykar and J. Xie, 'Finiteness properties of pseudo-hyperbolic varieties', International Mathematics Research Notices, 2020, published online. https://doi.org/10.1093/imrn/rnaa168

[Kaw80] Y. Kawamata, 'On Bloch's conjecture', *Invent. Math.* **57**(1) (1980), 97-100.

[Lan86] S. Lang, 'Hyperbolic and Diophantine analysis', *Bull. Amer. Math. Soc. (N.S.)* **14**(2) (1986), 159-205.

[Lan91] S. Lang, *Number Theory, III – Diophantine Geometry*, Encyclopaedia of Mathematical Sciences, 60 (Springer-Verlag, Berlin, 1991).

[Laz04] R. Lazarsfeld, *Positivity in Algebraic Geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete (3)*, **48** (Springer-Verlag, Berlin, 2004).

[Lev09] A. Levin, 'Generalizations of Siegel's and Picard's theorems', *Ann. of Math.* **(2)** **170**(2) (2009), 609-655.

[Man63] Ju. I. Manin, 'Proof of an analogue of Mordell's conjecture for algebraic curves over function fields', *Dokl. Akad. Nauk SSSR* **152** (1963), 1061-1063.

[McQ98] M. McQuillan, 'Diophantine approximations and foliations', *Publ. Math. Inst. Hautes Études Sci.* **87** (1998), 121-174.

[Nog82] J. Noguchi, 'A higher-dimensional analogue of Mordell's conjecture over function fields', *Math. Ann.* **258**(2) (1981/82), 207-212.

[Rou10] E. Rousseau, 'Hyperbolicity of geometric orbifolds', *Trans. Amer. Math. Soc.* **362**(7) (2010), 3799-3826.

[Ru97] M. Ru, 'On a general form of the second main theorem', *Trans. Amer. Math. Soc.* **349**(12) (1997), 5093-5105.

[RV20] M. Ru and P. Vojta, 'A birational Nevanlinna constant and its consequences', *Am. J. Math.* **142**(3) (2020), 957-991.

[Tur17] A. Turchet, 'Fibered threefolds and Lang-Vojta's conjecture over function fields', *Trans. Amer. Math. Soc.* **369**(12) (2017), 8537-8558.

[vBJK19] R. van Bommel, A. Javanpeykar and L. Kamenova, 'Boundedness in families with applications to arithmetic hyperbolicity', Preprint, 2019, arXiv:1907.11225.

[Voj11] P. Vojta, 'Diophantine approximation and Nevanlinna theory', in *Arithmetic Geometry, Lecture Notes in Mathematics*, 2009 (Springer, Berlin, 2011), 111-224.

[Voj87] P. Vojta, *Diophantine Approximations and Value Distribution Theory, Lecture Notes in Mathematics*, 1239 (Springer, Berlin, 1987).

[Voj97] P. Vojta, 'On Cartan's theorem and Cartan's conjecture', *Amer. J. Math.* **119**(1) (1997), 1-17.

[Wan04] J. T.-Y. Wang, 'An effective Schmidt's subspace theorem over function fields', *Math. Z.* **246**(4) (2004), 811-844.

[Yam15] K. Yamanoi, 'Holomorphic curves in algebraic varieties of maximal Albanese dimension', *Internat. J. Math.* **26**(6) (2015), 1541006.
[CZ08] P. Corvaja and U. Zannier, 'Some cases of Vojta's Conjecture on integral points over function fields', *J. Algebraic Geometry* **17** (2008), 195-333.

[CZ10] P. Corvaja and U. Zannier, 'Integral points, divisibility between values of polynomials and entire curves on surfaces', *Adv. Math.* **225**(2) (2010), 1095-1118.

[CZ13] P. Corvaja and U. Zannier, 'Algebraic hyperbolicity of ramified covers of $G_m^2$ (and integral points on affine subsets of $\mathbb{P}_2$)', *J. Differential Geom.* **93**(3) (2013), 355-377.

[Dem97] J.-P. Demailly, 'Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials', in *Algebraic geometry—Santa Cruz 1995, Proceedings of Symposia in Pure Mathematics*, 62, (American Mathematical Society, Providence, RI, 1997), 285-360.

[Fal94] G. Faltings, 'The general case of S. Lang’s conjecture', in *Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), Perspectives in Mathematics*, 15 (Academic Press, San Diego, 1994), 175-182.

[FM94] R. Friedman and J. W. Morgan, *Smooth Four-Manifolds and Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3)*, 27 (Springer-Verlag, Berlin, 1994).

[Gra65] H. Grauert, 'Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper', *Publ. Math. Inst. Hautes Études Sci.* **25** (1965), 131-149.

[GW19] J. Guo and J. T.-Y. Wang, 'Asymptotic gcd and divisible sequences for entire functions', *Trans. Amer. Math. Soc.* **371**(9) (2019), 6241-6256.

[HR18] S. Hussein and M. Ru, 'A general defect relation and height inequality for divisors in subgeneral position', *Asian J. Math.* **22**(3) (2018), 477-491.

[HS00] M. Hindry and J. H. Silverman, *Diophantine Geometry*, Graduate Texts in Mathematics, 201 (Springer-Verlag, New York, 2000). *An introduction*.

[HT00] J. Harris and Y. Tschinkel, 'Rational points on quartics', *Duke Math. J.* **104**(3) (2000), 477-500.

[HT01] B. Hassett and Y. Tschinkel, 'Density of integral points on algebraic varieties', in *Rational Points on Algebraic Varieties*, Progress in Mathematics, 199, (Birkhäuser, Basel, 2001), 169-197.

[JX20] A. Javanpeykar and J. Xie, 'Finiteness properties of pseudo-hyperbolic varieties', International Mathematics Research Notices, 2020, published online. https://doi.org/10.1093/imrn/rnaa168

[Kaw80] Y. Kawamata, 'On Bloch's conjecture', *Invent. Math.* **57**(1) (1980), 97-100.

[Lan86] S. Lang, 'Hyperbolic and Diophantine analysis', *Bull. Amer. Math. Soc. (N.S.)* **14**(2) (1986), 159-205.

[Lan91] S. Lang, *Number Theory, III – Diophantine Geometry*, Encyclopaedia of Mathematical Sciences, 60 (Springer-Verlag, Berlin, 1991).

[Laz04] R. Lazarsfeld, *Positivity in Algebraic Geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete (3)*, **48** (Springer-Verlag, Berlin, 2004).

[Lev09] A. Levin, 'Generalizations of Siegel's and Picard's theorems', *Ann. of Math.* **(2)** **170**(2) (2009), 609-655.

[Man63] Ju. I. Manin, 'Proof of an analogue of Mordell's conjecture for algebraic curves over function fields', *Dokl. Akad. Nauk SSSR* **152** (1963), 1061-1063.

[McQ98] M. McQuillan, 'Diophantine approximations and foliations', *Publ. Math. Inst. Hautes Études Sci.* **87** (1998), 121-174.

[Nog82] J. Noguchi, 'A higher-dimensional analogue of Mordell's conjecture over function fields', *Math. Ann.* **258**(2) (1981/82), 207-212.

[Rou10] E. Rousseau, 'Hyperbolicity of geometric orbifolds', *Trans. Amer. Math. Soc.* **362**(7) (2010), 3799-3826.

[Ru97] M. Ru, 'On a general form of the second main theorem', *Trans. Amer. Math. Soc.* **349**(12) (1997), 5093-5105.

[RV20] M. Ru and P. Vojta, 'A birational Nevanlinna constant and its consequences', *Am. J. Math.* **142**(3) (2020), 957-991.

[Tur17] A. Turchet, 'Fibered threefolds and Lang-Vojta's conjecture over function fields', *Trans. Amer. Math. Soc.* **369**(12) (2017), 8537-8558.

[vBJK19] R. van Bommel, A. Javanpeykar and L. Kamenova, 'Boundedness in families with applications to arithmetic hyperbolicity', Preprint, 2019, arXiv:1907.11225.

[Voj11] P. Vojta, 'Diophantine approximation and Nevanlinna theory', in *Arithmetic Geometry, Lecture Notes in Mathematics*, 2009 (Springer, Berlin, 2011), 111-224.

[Voj87] P. Vojta, *Diophantine Approximations and Value Distribution Theory, Lecture Notes in Mathematics*, 1239 (Springer, Berlin, 1987).

[Voj97] P. Vojta, 'On Cartan's theorem and Cartan's conjecture', *Amer. J. Math.* **119**(1) (1997), 1-17.

[Wan04] J. T.-Y. Wang, 'An effective Schmidt's subspace theorem over function fields', *Math. Z.* **246**(4) (2004), 811-844.

[Yam15] K. Yamanoi, 'Holomorphic curves in algebraic varieties of maximal Albanese dimension', *Internat. J. Math.* **26**(6) (2015), 1541006.