bio  website  homepage.sns.it/vistoli 

location  Italy  
age  57  
visits  member for  5 years, 5 months 
seen  Jun 22 at 17:56  
stats  profile views  19,834 
My name is Angelo Vistoli. I do algebraic geometry, mostly moduli theory.
Normally I don't answer questions from anonymous users. Lately I have lost interest, and hardly answered any question at all.
2d

awarded  Nice Answer 
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awarded  Enlightened 
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awarded  Nice Answer 
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awarded  Yearling 
Feb
8 
comment 
Do canonical stacks exist over Spec(Z)?
No, I don’t think that $S$ being regular is necessary to conclude that $U/H$ is smooth; flatness follows from the fact that $H$ is tame, and then smoothness can be checked on the fibers. The fact that $S$ is regular is used in the last step, when you normalize the fiber product $U \times_S V$, and use purity of the branch locus to conclude that it is étale over$U$ and $V$. 
Feb
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revised 
Do canonical stacks exist over Spec(Z)?
added 4 characters in body 
Feb
8 
answered  Do canonical stacks exist over Spec(Z)? 
Dec
3 
comment 
What is the expected dimension of the Zariski closure of the rational points on the moduli space of curves?
This follows from the CasnatiEkedahl description of coverings of degrees 4 and 5 (see G. Casnati, T. Ekedahl: Covers of algebraic varieties I. A general structure theorem, covers of degree 3,4 and Enriques' surfaces. J. Algebraic Geom., 5 (1996), pp. 439460, and G. Casnati: Covers of algebraic varieties II. Covers of degree 5 and construction of surfaces. J. Algebraic Geom., 5 (1996) pp 461477) together with the description of the stack of globally generated vector bundles on P^1 in M. Bolognesi, A. Vistoli, Stacks of trigonal curves, Trans. Amer. Math. Soc., 364 (2012), 3365–3393. 
Dec
1 
comment 
What is the expected dimension of the Zariski closure of the rational points on the moduli space of curves?
I believe that one can show that the stack of curves with a map of degree $d$ to a $\mathbb P^1$ is dominated by a rational variety for all $d \le 5$. This would give a lower bound $2g+5$ for the dimension of the closure. 
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awarded  Generalist 
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awarded  Good Answer 
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awarded  Explainer 
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awarded  Good Answer 
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awarded  Nice Answer 
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awarded  Curious 
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12 
awarded  Good Answer 
Mar
21 
awarded  Yearling 
Jan
13 
awarded  Enlightened 
Jan
13 
awarded  Nice Answer 
Dec
26 
awarded  Enlightened 