1.1. we typeset Hermitian (instead of hermitian) throughout this paper.
OK

1.2. we added parentheses (or a single parenthesis) throughout this paper.
OK

2.13. Remarks ... FOR CONSISTENCY WITH YOUR MODIFICATIONS TYPESET
i_*{\mathcal O}(\det(V*))

3.1. at line 1 of page 7 and line 8 (in page 23); should we typeset
``GGL Conjecture'' instead of ``GGL conjecture''. We thought that we
should keep as it is. OK

3.2. at the second line of Proposition 2.4 (in page 18); should we typeset
``$\mathrm{rank} (V) - 1$'' or ``$\mathrm{rank} (V - 1)$''?
$\mathrm{rank}(V) - 1$

3.3. at line 6 of page 27; should we typeset ``Property'' instead of
``property''? YES
ALSO TYPESET BEFORE
Properties 3.1 (i), (ii)
AND LATER
Property 3.1 (iii)

3.4. at the fifth line of Se t. 8 (in page 53); we typeset ``[GRe65]'' instead
of ``[GRec65]. OK

3.5. at the sixteenth line of page 54; could you advise please us where we
should typeset a losing parenthesis?
AS FOLLOWS:
projective algebraic);

3.6. at the ninth line of page 75; we typeset ``9.34'' instead of ``(9.34)''.

3.7. at lines (- 5) and (- 8) of page 78; should we typeset ``(n + 1) / 2'' or
``n + (1 / 2)''?
WHAT IS MEANT IS n+(1/2) BUT
n+\frac{1}{2}
LOOKS BETTER

3.8. for pages 79--81; should we keep the character ``,'' that appears after
$\eta$?
YES

3.9. at the eighth line of Subse t. 11.5 (in page 90); should we typeset
``$\mathrm{rank} (V) - 1$'' or ``$\mathrm{rank} (V - 1)$''?
$\mathrm{rank} (V) - 1$

3.10. at line (- 9) of page 94; we added ``as follows:''.
REPLACE BY "the following:"

3.11. at line (- 3) of page 100; should we typeset ``$\mathrm{dim} (Z) + 1$''
or ``$\mathrm{dim} (Z + 1)$''?
$2(\mathrm{dim} Z) + 1$
IS EVEN BETTER

3.12. in the middle of page 110; should we typeset the fractions using \frac
command? If yes, could you please advise us how to typeset them correctly?
USE
e^{n+\frac{1}{2}+\frac{1}{2n}}
AND
n^{n-\frac{3}{2}}
FORMULA BECOMES
$$b<\frac{n^{2n-1}\exp((2+\cdots+n)/n^2)}{\sqrt{2\pi n}\,(n/e)^n}<
\frac{e^{n+\frac{1}{2}+\frac{1}{2n}}}{\sqrt{2\pi}}\,n^{n-\frac{3}{2}}.$$

------------

page 22, YELLOW TAGS
DO NOT ADD "as follows" AS THIS IS GRAMMATICALLY INCORRECT
IF YOU REALLY WANT TO ADD SOMETHING, USE "the following", BUT THIS IS
UNNECESSARY.

------------

IN REMARK 3.4, REPLACE END OF PARAGRAPH BY:

Improving on this result of Clemens, Geng Xu [Xu94] proved that every
curve contained in a very generic surface of degree $d\ge 5$ satisfies
the sharp bound $g\ge d(d-3)/2-2$. In April~2018, I.~Coskun and
E.~Riedl improved the above bounds and got the more precise bound
$g\ge 1+(dk(d-5)+k)/2\,$; this result actually shows that a very
generic surface of degree $d\ge 5$ is algebraically hyperbolic in the
sense of Definition~3.2.  In higher dimension, L.~Ein ([Ein88],
[Ein91]) proved that every subvariety of a very generic hypersurface
$X\subset\bP^{n+1}$ of degree $d\ge 2n+1$ $(n\ge 2)$, is of general
type. This was reproved by a simple efficient technique by C.~Voisin
in [Voi96], along with other improvements.