# 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.

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### Weyl group and Galois action on cubic surfaces

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**1**answer

### K3 surfaces with small Picard number and symmetry

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### Characterization of an Abelian surface

**3**

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### Rational points on surfaces

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**1**answer

### Restriction of a Cartier divisor

**13**

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

**9**

**1**answer

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

**7**

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### Nef divisors on surfaces

**5**

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### Arnold's theorem on small denominators and holomorphic tubular neighborhoods

**2**

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### Cohomology of singular projective cubic surface

**3**

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### Abelian varieties corresponding to Hodge substructures

**3**

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### Articles of Casnati on algebraic varieties

**10**

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### Motivation for birational geometry

**4**

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### Newton polygon notation for algebraic surface singularities

**2**

**1**answer

### Behavior of canonical divisor under a finite group quotient

**1**

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### Rational classes of $(-2)$-curves in a minimal surface of general type

**2**

**1**answer

### Pseudoeffective divisors on surfaces

**1**

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### Elliptic fibrations on some Kummer surface in characteristic $2$

**3**

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### Log canonical surface with an elliptic singularity

**2**

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### Semi-stable sheaves on quadric surface

**2**

**1**answer

### When does the Hirzebruch surface have a nef anticanonical divisor?

**0**

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### $0$-cycles and $0$-cycles of degree $0$

**2**

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### Rational and rationally chain connected surfaces

**3**

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### Historical proof of Leschetz Hyperplane Theorem

**6**

**2**answers

### Representability of flat cohomology by a group scheme

**5**

**1**answer

### Volume of a divisor on a smooth projective surface

**2**

**1**answer

### Is the positive part of the Zariski decomposition of a big $\mathbb{R}$-divisor big?

**4**

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### Jacobians $\mathbb{F}_q$-isogenous to the direct square of an ordinary elliptic $\mathbb{F}_q$-curve of $j$-invariant $0$

**3**

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### Singular del Pezzo surfaces and degeneration of root systems

**2**

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### description of very ample bundle of Hirzebruch surface

**1**

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### Surfaces of general type with $h^1(-K_X)\neq 0$

**3**

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### "Simplification" of the map constructed at the proof of Castelnuovo's contractibility theorem

**0**

**1**answer

### Intersection of the tautological bundle with a fiber of a geometrically ruled surface

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

**7**

**1**answer

### General conditions for normality of blow-up

**8**

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

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### Is the surface in $\mathbb{A}^3$ rational?

**5**

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### Surface of type $(2,2)$ on the Segre cubic scroll $\mathbb{P}^1 \times \mathbb{P}^2 \subset \mathbb{P}^5$

**4**

**1**answer

### Existence of perfect Morse functions on Fermat surfaces $x^n+y^n+z^n+w^n=0$

**5**

**2**answers

### Generalisations of Riemann-Roch for surfaces

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### nonvanishing higher cohomology of a very ample divisor

**13**

**1**answer

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

**4**

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### Reducible surface as a degeneration

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### Minimal model vs canonical model of a surface

**6**

**2**answers

### Smooth projective surface with geometrically integral reduction

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### arithmetic del Pezzo surfaces in comparison with del Pezzo surfaces over a field

**1**

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### Non-isotrival fiber bundle over compact Riemann surface

**10**

**1**answer

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

**1**

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### On a quadratic diophantine equation

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