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

4 votes
1 answer
281 views

Are automorphism groups of polarized varieties of finite type

It is "well-known" that the stack of polarized varieties is an algebraic stack with quasi-compact and separated diagonal. In particular, if $(X,L)$ and $(Y,M)$ are polarized schemes over a scheme $S$ …
Pancho's user avatar
  • 171
6 votes
0 answers
254 views

Is the stack of varieties with a big line bundle algebraic

In Starr's paper https://www.math.stonybrook.edu/~jstarr/papers/moduli4.pdf the folk result that the fibred category of pairs $(X\to S, L)$, where $S$ is an affine scheme, $X\to S$ is flat proper fini …
Pancho's user avatar
  • 171
7 votes
1 answer
887 views

Isotrivial families with non-zero Kodaira spencer map

Let $S$ be a smooth quasi-projective curve over the complex numbers. Let $P$ be a closed point in $S$. Let $f:\mathcal X \to S$ be a polarized family of smooth projective connected varieties. To this …
Pancho's user avatar
  • 171