bio | website | homepage.sns.it/vistoli |
---|---|---|
location | Italy | |
age | 56 | |
visits | member for | 5 years, 2 months |
seen | yesterday | |
stats | profile views | 19,614 |
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. |