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

4 votes
1 answer
250 views

Kodaira dimension of the base

I am looking for a proof of the following statement: Let $f: X \to B$ be a surjective morphism between smooth projective varieties such that $-K_X$ is nef and $B$ is non-uniruled then Kodaira dimensi …
1984's user avatar
  • 189
3 votes
0 answers
314 views

Examples such that Albanese morphism is not well-defined

Let $X$ be a compact Kahler space(Kahler variety), then it is known that the Albanese morphism $alb_X:X\to Alb(X)$ is a well-defined morphism when $X$ has at worst rational singularities. It there so …
1984's user avatar
  • 189
10 votes
1 answer
593 views

Maximal Albanese variety

I am looking for a proof for the following statement A smooth projective variety $X$ has maximal Albanese dimension if and only if the cotangent bundle of $X$ is generically generated by its …
1984's user avatar
  • 189
0 votes
0 answers
165 views

Surjectivity of the Albanese map of the moduli space of stable vector bundles

I have a naive question:(I saw that it is related to relative K-theory of Hodge-Deligne and also Nadel-Chern-Weil theory ) Let $\mathcal M (r, d)$ be the moduli space of stable vector bundles of rank …
1984's user avatar
  • 189