5,066 reputation
11532
bio website dm.unipi.it/~pardini
location Italy
age
visits member for 4 years
seen Nov 16 at 11:48
My name is Rita Pardini. I work in classical algebraic geometry, mainly surfaces.

Nov
8
answered Kummer Coverings
Nov
6
awarded  Yearling
Sep
24
awarded  Autobiographer
Jul
8
comment smooth quotient out of a singular variety?
I forgot irreducible, sorry!
Jul
8
comment smooth quotient out of a singular variety?
A variation of this answer in order to satisfy Libli's request that the example be quasi-projective: take $X$ the union of two planes of $\mathbb C^4$ intersecting at the origin and let $\mathbb Z_2$ act by identifying the two planes via any linear isomorphism. $X$ is affine and behaves as Dan's example.
Jul
2
awarded  Curious
Jun
28
awarded  Popular Question
Mar
4
comment Does $h^1(D)=0$ imply numerical connectedness on K3 surfaces?
Ciao Pigna! welcome to MO!
Mar
4
comment Does $h^1(D)=0$ imply numerical connectedness on K3 surfaces?
No. For instance if $A$ is a a rational curve with $A^2<0$, then $h^0(\mathcal O_A(-A))>0$.
Dec
29
comment (Non-)Existence of curves of low degree on affine and projective varieties
The Noether Lefschetz theorem says that the Picard group of a very general surface of degree $d\ge 4$ of $\mathbb P^3$ is cyclic generated by the hyperplane section, so in this case all curves have degree divisible by $d$. ("Very general" means "in the complement of a countable union of Zariski closed subsets").
Nov
6
comment Etale covers of products of curves
For completeness, one needs to show that the unramified cover is not itself a product of curves. If, for instance, $C_1'$ and $C'_2$ have the same genus and $|G|=2$, this can be seen by computing $h^1(\mathcal O)$ and $h^2(\mathcal O)$.
Nov
6
awarded  Yearling
Oct
14
comment Complete Linear system on Del Pezzo surfaces
My feeling is that the statement might be correct (I thought about it a bit couldn' find a counterexample), but I wouldn't know how to prove it.
Oct
12
revised Complete Linear system on Del Pezzo surfaces
added 11 characters in body
Oct
12
revised Complete Linear system on Del Pezzo surfaces
added 110 characters in body
Oct
12
comment Complete Linear system on Del Pezzo surfaces
If you are interested in a precise example of linear system, it may be possible to answer the question by using numerical considerations, but asking about the intersection of the components in general does not make much sense.
Oct
12
answered Complete Linear system on Del Pezzo surfaces
Oct
11
awarded  Constituent
Oct
1
awarded  Caucus
Sep
26
comment Quotient of an abelian surface by an antisymplectic involution
@Misha: the map that switches factors is antisymplectic, since $dx\wedge dy$ goes to $dy\wedge dx$.