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Results tagged with ag.algebraic-geometry
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user 15415
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
4
votes
1
answer
216
views
relationship between freeness and nefness of a rational curve
I'm not able to figure out the precise relation between nefness and freeness
of a rational curve $C$ on a projective variety $X$.
A curve is said to be nef if it intersects non-negatively every effe …
- 135
3
votes
0
answers
120
views
Codimension of $\text{Sing}(\overline{\mathcal{K}}_g)$ in $\overline{\mathcal{K}}_g$
Hi everybody,
let $\mathcal{P}_g$ be the moduli stack parametrizing pairs $(S,C)$ where $S$ is a K3 surface with a primitive polarization $L$ of genus $g$ and $C \in |L|$ is a smooth curve of genus $ …
- 135
3
votes
1
answer
286
views
Decomposition of $f^{*}T_X$ for a morphism $f:\mathbb{P}^1 \rightarrow X$
Hi everybody,
let $X$ be a smooth projective variety of dimension $n$ and let $f:\mathbb{P}^1 \rightarrow X$ be a morphism.
A theorem of Grothendieck says that the vector bundle $f^{*}T_X$ splits as …
- 135
2
votes
1
answer
271
views
Rational map associated to a big and nef divisor
Let $D$ be a big and nef divisor on a smooth complex projective minimal surface and let $\phi_D$ be the induced rational map. Is it true that $\phi_D$ is generically finite? Otherwise does someone kno …
- 135
1
vote
0
answers
113
views
relation between $C \cdot K_S$ and $K^2_S$ for a curve $C$ on a complete intersection surfac...
Let $S$ be a smooth complex projective surface which is a complete intersection and such that $K_S=\mathcal{O}_S(k)$, $k >0$.
Let $C$ be a smooth curve on $S$ such that $C^2 >0$.
I'm interested in a …
- 135