Let $K$ be a field of characteristic zero but not algebraically closed. Let $C$ be a smooth projective curve over $K$. Let $r, d$ be two positive integers that are coprime. Consider the moduli space of stable vector bundles of degree $d$ and rank $r$ over $C$. Is it fano? If so could someone suggest a reference for this fact.

Let $K$ be a field of characteristic zero but not algebraically closed. Let $C$ be a smooth projective curve over $K$. Let $r, d$ be two positive integers that are coprime. Consider the moduli space of stable vector bundles of degree $d$ and rank $r$ over $C$ with fixed determinantal line bundle. Is it fano? If so could someone suggest a reference for this fact.

Let $K$ be a characteristic zero field but not algebraically closed. Let $C$ be a smooth projective curve over $K$. Let $r, d$ be two positive integers that are coprime. Consider the moduli space of stable vector bundles of degree $d$ and rank $r$ over $C$. Is it fano? If so could someone suggest a reference for this fact.

Let $K$ be a field of characteristic zero but not algebraically closed. Let $C$ be a smooth projective curve over $K$. Let $r, d$ be two positive integers that are coprime. Consider the moduli space of stable vector bundles of degree $d$ and rank $r$ over $C$. Is it fano? If so could someone suggest a reference for this fact.