21,143 reputation
26089
bio website homepage.sns.it/vistoli
location Italy
age 57
visits member for 5 years, 3 months
seen Jun 22 at 17:56

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.


Mar
21
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
8
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 Casnati-Ekedahl 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. 439-460, and G. Casnati: Covers of algebraic varieties II. Covers of degree 5 and construction of surfaces. J. Algebraic Geom., 5 (1996) pp 461-477) 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.
Nov
13
awarded  Generalist
Oct
7
awarded  Good Answer
Sep
30
awarded  Explainer
Aug
26
awarded  Good Answer
Jul
14
awarded  Nice Answer
Jul
2
awarded  Curious
May
12
awarded  Good Answer
Mar
21
awarded  Yearling
Jan
13
awarded  Enlightened
Jan
13
awarded  Nice Answer
Dec
26
awarded  Enlightened
Dec
26
awarded  Nice Answer
Sep
16
awarded  Guru
Sep
15
comment Descent for group actions
Sorry, I had not read the question properly, I thought that $G$ was the Galois group.