# Questions tagged [k3-surfaces]

For all questions about *K3 surfaces*, that is complex or algebraic smooth surfaces which are regular with trivial canonical bundle.

11 questions
Filter by
Sorted by
Tagged with
0answers
45 views

### Global sections of a line bundle associated to a smooth irreducible curve on a K3 surface.

I would like to know it the following proof is correct: Lemma: Let $C$ be a smooth, irreducible curve of genus $g$ over a complex projective K3 surface $X$. Let $L:=\mathcal{O}_X(C)$. Then $C^2=2g-2$...
0answers
40 views

### Completions of Stalks of a Surface

Let S be a surface (so a 2-dimensional proper k-scheme). My question arises from following another thread of mine: https://mathoverflow.net/questions/331251/intuition-behind-rdp-rational-double-points ...
0answers
40 views

### Kähler Potential on Blowup of $\mathbb{C}/\{\pm 1\}$

The book Joyce: Riemannian Holonomy Groups and Calibrated Geometry contains on page 205 the Eguchi-Hanson space as an example: Consider $\mathbb{C}^2$ with complex coordinates $(z_1,z_2)$, acted ...
1answer
88 views

### blowing-up preserves the first Betti number?

Let $G$ be a finite group and $S$ be a K3 surface. $G$ acts effectively and symplectically(fix the nowhere vanishing 2-form of $S$) on $S$. Since the action is symplectic,quotient surface $S/G$ has ...
0answers
33 views

### Any concrete example(s) of $K3$ surfaces with Picand number 18 and does not admit Shioda-Inose structure?

I am looking for some explicit examples of (elliptic) $K3$-families defined over a number field (better to be over $\mathbb{Q}$) with Picard number $18$ but does not admit Shioda-Inose structure, i.e. ...
0answers
109 views

### Is the Calabi-Yau property of a smooth manifold a differential invariant?

In this question I asked if it could happen that two complex manifolds are homeomorphic, and one of them is a Calabi-Yau manifold but the other isn't. It turns out that there are complex surfaces that ...
1answer
165 views

### Can a complex manifold that is not a Calabi-Yau manifold be homeomorphic to a Calabi-Yau manifold?

This is a kind of a follow up to this question, which actually already had an answer here, in which it is asserted that Hodge numbers in general are not topological invariants. Could it be so extreme ...
2answers
223 views