# Tag Info

## Hot answers tagged ag.algebraic-geometry

### Bott & Tu differential forms Example 10.1

In my version of Bott and Tu, the example reads (emphasis mine): "Moreover, if $V \subset U$ is an inclusion of CONTRACTIBLE open sets, then $\rho^U_V: H^q(\pi^{-1} U) \to H^q( \pi^{-1} V)$ is an ...
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### Bad prime of torsor and original elliptic curve ; Definition of Tate–Shafarevich group $Ш(E/K)$

I fear you wish for too much here. If $Ш$ is finite, then we can represent each element by a torsor; each torsor has good reduction away from a finite set and the union of all bad places would then be ...
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### Exceptional locus of rational map has codimension two

This not true. The simplest counterexample is the linear projection $Q \dashrightarrow \mathbb{P}^2$ from a smooth quadric surface $Q \subset \mathbb{P}^3$ from a point. The inverse map blows up two ...
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### What is the length of an algebraic curve?

Let me just clarify the proof Boris Bukh was thinking of in the question you link. Let $d$ be the degree of the curve, then the length of $Z \cap D_r(0)$ is at most $\pi r d$. Consider a series of ...
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### Making a map in sheaf cohomology involving a theta characteristic explicit

I claim that I can give a reasonably "geometric" formula. Consider the surface $C \times C$ and the diagonal $\Delta$. The the line bundle $\vartheta \boxtimes \vartheta$ has vanishing ...
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First, we note that the coherator on an affine scheme is given by the associated quasi-coherent sheaf to the global section (cf. Thomason-Trobaugh, Appendix B. 14). Let $A$ be a ring. Write \$S :\...