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Results tagged with ag.algebraic-geometry
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user 75343
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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123
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Bilinear form and double cover
Let $\pi:X\rightarrow Y$ be a double cover of curves (smooth and projective), and $E$ a vector bundle on $X$ with a non-degenerate symmetric bilinear form $\phi:E\otimes E\rightarrow \mathcal O_X$. Wi …
- 307
4
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96
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Dual involution on the $Ext^1$
Let $X$ be a smooth algebraic curve over $\mathbb C$, and let $F$ be a vector bundle on it of degree $1$, take the dual of an extention $$0\rightarrow F^*\rightarrow E\rightarrow F\rightarrow0$$ is ag …
- 307
1
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98
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critiria to prove that a morphism is an embedding
I have a forgetful map between moduli spaces, I want to prove that it is an embedding, In fact, I have a reductive algebric group (which is not constant) over a curve $X$ whose geniric fiber is semisi …
- 307
4
votes
1
answer
207
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Vector bundles with symmetric perfect form
Let $X$ be a smooth projective curve, and $E$ a vector bundle on $X$ such that there exist a bilinear perfect symmetric form $$E\otimes E\rightarrow \mathcal O_X$$
When I see $E$ as a $GL_r$ princi …
- 307