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Charles Matthews
Charles Matthews
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Real Algebraic Varietyalgebraic variety and Realreal algebraic Bundlebundle

Let $X$ be a scheme definedefined over $\mathbb{C}$ with an involution $\sigma$. Then howHow to get a $X_{\mathbb{R}}$ scheme definedefined over $\mathbb{R}$ such that $X_{\mathbb{R}}\times_\mathbb{R} \mathbb{C} = X$ ? How are the real algebraic bundle on $X_{\mathbb{R}}$ and complex bundle on $X$ are related?

Real Algebraic Variety and Real algebraic Bundle

Let $X$ be a scheme define over $\mathbb{C}$ with an involution $\sigma$. Then how to get a $X_{\mathbb{R}}$ scheme define over $\mathbb{R}$ such that $X_{\mathbb{R}}\times_\mathbb{R} \mathbb{C} = X$ ? How the real algebraic bundle on $X_{\mathbb{R}}$ and complex bundle on $X$ are related?

Real algebraic variety and real algebraic bundle

Let $X$ be a scheme defined over $\mathbb{C}$ with an involution $\sigma$. How to get a $X_{\mathbb{R}}$ scheme defined over $\mathbb{R}$ such that $X_{\mathbb{R}}\times_\mathbb{R} \mathbb{C} = X$ ? How are the real algebraic bundle on $X_{\mathbb{R}}$ and complex bundle on $X$ related?

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Yashica
Yashica
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Real Algebraic Variety and Real algebraic Bundle

Let $X$ be a scheme define over $\mathbb{C}$ with an involution $\sigma$. Then how to get a $X_{\mathbb{R}}$ scheme define over $\mathbb{R}$ such that $X_{\mathbb{R}}\times_\mathbb{R} \mathbb{C} = X$ ? How the real algebraic bundle on $X_{\mathbb{R}}$ and complex bundle on $X$ are related?