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Actually, it is possible to prove the following statement. Set

$$\mathbb{N}(L, X):=\{a > 0 \ | \ h^0(X, aX) \geq 1 \}$$

and let $d$ be the largest common divisor of $\mathbb{N}(L, X)$.

Then there exist two positive integers $\alpha$, $\beta$ such that for $m$ large enough one has

$$\alpha m^{k(L)}\leq h^0(X, mdL) \leq \beta m^{k(L)}.$$

For a proof, see [Ueno, Classification theory of algebraic varieties and compact complex manifolds, Lecture Notes in Mathematics 439, Theorem 8.1 p. 86].

Actually, it is possible to prove the following statement. Set

$$\mathbb{N}(L, X):=\{a > 0 \ | \ h^0(X, aL) \geq 1 \}$$

and let $d$ be the largest common divisor of the elements of $\mathbb{N}(L, X)$.

Then there exist two positive integers $\alpha$, $\beta$ such that for $m$ large enough one has

$$\alpha m^{k(L)}\leq h^0(X, mdL) \leq \beta m^{k(L)}.$$

For a proof, see [Ueno, Classification theory of algebraic varieties and compact complex manifolds, Lecture Notes in Mathematics 439, Theorem 8.1 p. 86].

Actually, it is possible to prove the following statement. Set

$$\mathbb{N}(L, X):=\{m > 0 \ | \ h^0(X, mX) \geq 1 \}.$$

Then there exist two positive integers $\alpha$, $\beta$ such that for $m$ large enough one has

$$\alpha m^{k(L)}\leq h^0(X, mdL) \leq \beta m^{k(L)}.$$

where $d$ denotes the largest common divisor of $\mathbb{N}(L, X)$.

For a proof, see [Ueno, Classification theory of algebraic varieties and compact complex manifolds, Lecture Notes in Mathematics 439, Theorem 8.1 p. 86].

Actually, it is possible to prove the following statement. Set

$$\mathbb{N}(L, X):=\{a > 0 \ | \ h^0(X, aX) \geq 1 \}$$

and let $d$ be the largest common divisor of $\mathbb{N}(L, X)$.

Then there exist two positive integers $\alpha$, $\beta$ such that for $m$ large enough one has

$$\alpha m^{k(L)}\leq h^0(X, mdL) \leq \beta m^{k(L)}.$$

For a proof, see [Ueno, Classification theory of algebraic varieties and compact complex manifolds, Lecture Notes in Mathematics 439, Theorem 8.1 p. 86].

Actually, it is possible to prove that there exist two positive integers $\alpha$, $\beta$ such that for $m$ large enough one has

$$\alpha m^{k(L)}\leq h^0(X, mL) \leq \beta m^{k(L)}.$$

For a proof, see [Ueno, Classification theory of algebraic varieties and compact complex manifolds, Lecture Notes in Mathematics 439, Theorem 8.1 p. 86].

Actually, it is possible to prove the following statement. Set

$$\mathbb{N}(L, X):=\{m > 0 \ | \ h^0(X, mX) \geq 1 \}.$$

Then there exist two positive integers $\alpha$, $\beta$ such that for $m$ large enough one has

$$\alpha m^{k(L)}\leq h^0(X, mdL) \leq \beta m^{k(L)}.$$

where $d$ denotes the largest common divisor of $\mathbb{N}(L, X)$.

For a proof, see [Ueno, Classification theory of algebraic varieties and compact complex manifolds, Lecture Notes in Mathematics 439, Theorem 8.1 p. 86].