20,688 reputation
25989
bio website homepage.sns.it/vistoli
location Italy
age 56
visits member for 4 years, 9 months
seen Dec 5 at 18:56
My name is Angelo Vistoli. I do algebraic geometry, mostly moduli theory.

Normally I don't answer questions from anonymous users.

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.
Sep
15
comment Descent for group actions
It always descends to the space of invariants in $V$.
Sep
13
answered Determine complex analytic germ along a smooth compact curve via normal bundle?
Aug
16
awarded  Nice Answer
Aug
9
comment Can I conclude that a morphism of vector bundles is zero if it is so fiberwise?
Consider the case that $X = Y$, $f = \mathrm{id}_X$, $\cal U = \cal V = \cal O$, and $X$ is not reduced.