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Results tagged with ag.algebraic-geometry
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user 37622
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
11
votes
A double cover of $\mathbb{P}^n \times \mathbb{P}^n$
The answer is no. The reason is that the Picard group of a complete intersection of dimension $\ge 3$ in a weighted projective space is of rank 1 and the Picard group of the double cover is of rank $\ …
- 416
1
vote
Surfaces in $\mathbb P^3$ with many simple isolated singularities
For the case of surfaces of degree $\le 6$, you may consult
Catanese, F.; Ceresa, G.:
J. Pure Appl. Algebra 23 (1982), and, if you read Italian,
Ezio Stagnaro:
Rend. Sem. Mat. Univ. Padova 59 (197 …
- 416
1
vote
Accepted
A question on existence of degeneration of Enriques surface.
The surface $S_1$ is rational and the surface is an elliptic ruled surface (induced by the projection $E\times \mathbb{P}^1\to E$). The glued surface is a standard Type II degeneration of Enriques su …
- 416
1
vote
Dimension of the space of invariant quadratic differentials in Galois covers
You may get what you need from various papers on the equivariant Riemann-Roch theorem applied to your G-linearized sheaf $T_X$. For example, look at the papers of Borne and/or Ellingsrud-Lonstead.
- 416
2
votes
General curves of genus 3 as plane sections of Kummer surfaces
The paper by Alessandro Verra (Math. Ann. 276 (1987), no. 3, 433–448) gives a very precise description of all fibers of the Prym map $\mathcal{R}_3\to \mathcal{A}_2$ from which the answer to your que …
- 416
2
votes
Is the moduli space of stable vector bundles over a smooth projective curve fano?
Yes, if $g > 1$, it is Fano because its Picard group (over algebraic closure, and hence over K) is isomorphic to $\mathbb{Z}$. You can find the needed references , for example, in
Drezet and Narasi …
- 416
3
votes
Effectiveness of the distinguished theta characteristic in characteristic 2
Let $F:X\to X$ be the relative Frobenius morphism. It is a finite morphism of degree $2$, and we have an exact sequence
$$0\to \mathcal{O}_X\to F_*\mathcal{O}_X \to L \to 0$$
for some invertible shea …
- 416
3
votes
Accepted
Reference for Automorphisms of K3 surfaces
You may consult
Kondō, Shigeyuki Quadratic forms and K3. Enriques surfaces [translation of Sûgaku 42 (1990), no. 4, 346–360; MR1083944 (92b:14018)]. Sugaku Expositions. Sugaku Expositions 6 (1993), n …
- 416
3
votes
Accepted
How to explicitly see the ramification over infinity
One way to see this is the following. Let $U$ be the complement of the points $t_1,\ldots,t_n$ in $\mathbb{P}^1(\mathbb{C})$. The fundamental group $\pi_1(U)$ is generated by elements $\gamma_1,\ldots …
- 416