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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

5 votes
Accepted

Looking for a special rank 2 vector bundle

Every curve admits a degree g-1 line bundle with $h^0=h^1=0$ -- in fact a generic degree g-1 line bundle has this property, since the space of degree g-1 divisors is g-1 dimensional, but the space of …
Tom Graber's user avatar
6 votes
Accepted

Does negative semidefinite intersection matrix of bunch of curves implies zero intersection ...

The answer already given here seems to assume the E_i are pairwise disjoint, which I didn't take to be the case from your question. To get the result in general, I think you need to use the additiona …
Tom Graber's user avatar
6 votes

Intersection on Singular Varieties

Normal is not enough to define an intersection product in higher dimensions. In Fulton, I think you can find the example of a cone over a quadric surface on which it is impossible to define a well be …
Tom Graber's user avatar
12 votes
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What is the minimal degree of a smooth projective embedding of a hyperelliptic curve?

Felipe, I believe the answer here is d=g+3. To see that you can embed your curve in this degree is straightforward - just choose a generic line bundle of degree g+3 and it will work. In the case of …
Tom Graber's user avatar