# Questions tagged [birational-geometry]

Birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.

**9**

**2**answers

### Reference request on birational invariance of Chow group of zero cycles of degree zero

**17**

**3**answers

### Contracting divisors to a point

**13**

**2**answers

### Training towards research on birational geometry/minimal model program

**16**

**1**answer

### Applications of derived categories to “Traditional Algebraic Geometry”

**12**

**2**answers

### Blowups of Cohen-Macaulay varieties

**6**

**1**answer

### Top self-intersection of exceptional divisors

**7**

**3**answers

### Pseudo-automorphisms on Fano varieties

**6**

**1**answer

### Why is the inverse of a bijective rational map rational?

**3**

**2**answers

### Irreducible divisor in a basepoint free linear system

**7**

**1**answer

### Proving a variety is not unirational

**5**

**1**answer

### Automorphisms of Cartesian products

**4**

**0**answers

### What is the fundamental group of Kontsevich's space of stable maps?

**4**

**1**answer

### Discussion of Luroth's problem in an article of Beauville

**2**

**2**answers

### Numerically negative exceptional divisor on a surface.

**7**

**0**answers

### References about conic bundles

**7**

**1**answer

### Is there a purely inseparable covering $\mathbb{A}^2 \to K$ of a Kummer surface $K$ over $\mathbb{F}_{p^2}$?

**5**

**1**answer

### Singularities of fibrations

**4**

**0**answers

### Can Kummer surfaces coming from the same abelian surface be Cremona equivalent / isomorphic?

**4**

**1**answer