# Questions tagged [algebraic-surfaces]

An algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of dimension four as a smooth manifold.

**38**

**5**answers

### Surfaces in $\mathbb{P}^3$ with isolated singularities

**35**

**1**answer

### When do 27 lines lie on a cubic surface?

**29**

**1**answer

### Enriques surfaces over $\mathbb Z$

**27**

**1**answer

### Analogies between classical geometry on complex surfaces and Arakelov geometry

**26**

**5**answers

### blowing up, -1 curves, effective and ample divisors

**23**

**4**answers

### Abundance for algebraic surfaces

**23**

**3**answers

### Hyperbolic Coxeter polytopes and Del-Pezzo surfaces

**23**

**1**answer

### Del Pezzo surfaces and homotopy groups of spheres

**22**

**0**answers

### bound on the genus of a fiber of the Albanese map of a surface with $h^1({\mathcal O})=1$?

**19**

**3**answers

### Vector bundles on $\mathbb{P}^1\times\mathbb{P}^1$

**18**

**2**answers

### When does the blow-up of $CP^2$ at N points embed in $CP^4$?

**16**

**1**answer

### what is the cyclic cover trick?

**16**

**0**answers

### A question on surfaces in $\mathbb{P}^4$

**15**

**6**answers

### Curves with negative self intersection in the product of two curves

**15**

**4**answers

### K3 surfaces with good reduction away from finitely many places

**15**

**1**answer

### Is the set of surfaces over Spec Z with ample canonical sheaf empty

**14**

**4**answers

### Rational curves on varieties of general type

**14**

**2**answers

### Surfaces containing curves of arbitrarily negative self-intersection

**14**

**4**answers

### Algebraic surfaces and their (intrinsic) geometry

**14**

**0**answers

### Ample divisors on projective surfaces

**13**

**3**answers

### A nontrivial surface on which any two curves intersect

**13**

**1**answer

### Are any of these complex surfaces ever projective?

**12**

**0**answers

### Curves on rational surfaces and Lang's conjecture for M_g

**11**

**3**answers

### Nonprojective Surface

**11**

**3**answers

### level sets of multivariate polynomials

**11**

**1**answer

### Euler Characteristic of Real Algebraic Surfaces

**11**

**0**answers

### Surfaces with $q=2$ and generically finite Albanese map

**11**

**0**answers

### Singular curve on an abelian surface

**10**

**2**answers

### Motivation for birational geometry

**10**

**2**answers

### Uniformization of Kodaira fibered surfaces

**10**

**1**answer

### Restriction of the Picard group of a surface to a curve

**10**

**1**answer

### Automorphisms of del Pezzo surfaces

**10**

**1**answer

### A diffeomorphism of complex surfaces mapping subvarieties to subvarieties

**10**

**1**answer

### When is the canonical divisor of an algebraic surface smooth?

**10**

**1**answer

### A proper smooth surface is projective

**10**

**1**answer

### A property of varieties between unirational and retract rational

**9**

**1**answer

### Pathologies of analytic (non-algebraic) varieties.

**9**

**1**answer

### Pull-back of an irreducible ample divisor via an isogeny of abelian varieties

**9**

**1**answer

### Does $X\times Y$ have the resolution property if both $X$ and $Y$ have?

**9**

**1**answer

### Are there non-projective normal surfaces which are rational?

**9**

**1**answer

### Dimension-specific phenomena in algebraic geometry

**9**

**0**answers

### How many characteristics is a random surface unirational in?

**8**

**2**answers

### Is the square of a curve minus its diagonal affine?

**8**

**1**answer

### Finite morphisms to projective space

**8**

**3**answers

### Cone of curves and Mori theorem for algebraic surfaces

**8**

**1**answer

### Why can you deform singularities in two dimensions but not in higher dimensions?

**8**

**1**answer

### Contracting a curve of negative self-intersection on a surface

**8**

**1**answer

### Is the Tate conjecture known for etale covers of products of curves

**8**

**2**answers

### Blow-up of the plane at $5$ points

**8**

**1**answer