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

5 votes
Accepted

Log smooth models for abelian varieties

This question has been answered in the following preprint: http://arxiv.org/abs/1512.02464
Arne Smeets's user avatar
6 votes
1 answer
448 views

Log smooth models for abelian varieties

Let $K$ be a field complete for a discrete valuation. Assume that the residue field has characteristic $p > 0$. Let $A$ be an abelian variety over $K$ having the property that (for some prime $\ell \n …
Arne Smeets's user avatar
5 votes
3 answers
2k views

Vanishing of the top Chern class of a vector bundle

Let $X$ be a smooth, projective variety over $\mathbf{C}$ (to keep things simple) and let $\mathcal{F}$ be a vector bundle on $X$. If $\mathcal{F}$ has a nowhere vanishing holomorphic section, the t …
Arne Smeets's user avatar
7 votes
1 answer
602 views

Hyperplane sections with chi non-zero

Let $X$ be a smooth, projective variety over $\mathbb{C}$ for which $\chi(X) = 0$. Here by $\chi$, I mean the topological Euler characteristic of $X(\mathbb{C})$; this number can also be computed as t …
Arne Smeets's user avatar