[Search] |

ABOUT:
[Introduction]POINTERS:
[Texts]## 14J: Surfaces and higher-dimensional varieties |

- 14J05: Picard group, See also 14C22, 19A49, 32L05 [to be dropped from MSC2000]
- 14J10: Families, moduli, classification: algebraic theory
- 14J15: Moduli, classification: analytic theory, See also 32G13, 32J15
- 14J17: Singularities of surfaces
- 14J20: Arithmetic ground fields, See also 11Dxx, 11G25, 11G35, 14Gxx
- 14J25: Special surfaces, For Hilbert modular surfaces, See 14G35
- 14J26: Rational and ruled surfaces
- 14J27: Elliptic surfaces
- 14J28: K3 surfaces and Enriques surfaces
- 14J29: Surfaces of general type
- 14J30: [Special] 3-folds, See also 14E05
- 14J32: Calabi-Yau manifolds, mirror symmetry [new in 2000]
- 14J35: [Special] 4-folds, See also 14E05
- 14J40: [Special] n-folds (n > 4)
- 14J45: Fano varieties
- 14J50: Automorphisms of surfaces and higher-dimensional varieties. See also 14E09
- 14J60: Vector bundles on surfaces and higher-dimensional varieties. See also 14F05, 32Lxx
- 14J70: Hypersurfaces
- 14J80: Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) [new in 2000]
- 14J81: Relationships with physics [new in 2000]
- 14J99: None of the above but in this section

Parent field: 14 - Algebraic geometry

Browse all (old) classifications for this area at the AMS.

- Describing the family of reducible cubic surfaces among all cubic surfaces (hopeless?)
- What can an algebraic surface in R^3 look like?
- What can a quadratic surface in R^3 look like?
- A surface may be presented as fibred over a curve, with fibres of different genera.
- How can you tell if an algebraic surface is rational over a specific field?
- There are infinitely many rational points on the Euler ("Fermat") surface x^4+y^4+z^4=1; is there a parameterized family? (Open)
- Solutions to x^3 + y^3 = z^2
- Sum of two fifth powers a square?
- Small generalization of FLT: x^n + y^n = z^m has solutions iff gcd(n,m)=1 or n=m=2.
- The Beal conjecture: solutions to x^n + y^m = z^r
- Solutions to generalized Fermat equation x^a+y^b=z^c.
- Examples of pairs of perfect powers which sum to another perfect power.
- There are infinitely many solutions to x^2 + y^3 = z^4
- Solutions to A x^p + B y^q = C z^r? (none with A=B=C=1 if p,q,r greater than 2)
- Which is larger: a^(1/3) or b^(1/3)+c^(1/3) (remarkable close calls are solutions to |(a-b-c)^3-27abc|=1)
- Parameterizing the solutions to x^3+y^3+z^3+w^3=0
- Solving the pair x^2 + y^2 = u^4, x+y = v^2 in integers.
- Seeking integral points on the intersections of 3 quadratics in P^4.
- A few near misses of solutions to the Integral Brick problem.
- The rational box: still open
- Update on searches for a rational box.
- Rational boxes with weakened conditions to be met
- The spider-on-a-box problem: there are parameterized families of integer boxes with all three geodesic distances between opposite corners being integral too.
- How many normals to a surface meet at a point?
- Parameterizing the family of lines tangent to two spheres (an algebraic surface).
- "Freshman addition of reciprocals": 1/(A+B+C+D) = (1/A) + (1/B) + (1/C) + (1/D)
- The hyperbolic Pythagorean theorem, a^2 + b^2 = c^2 * (1+a^2*b^2)
- Two squares from two numbers: finding a and b so that a+b^2 and b+a^2 are both squares.
- Four squares from three integers: can ab+1, bc+1, ca+1, and abc+1 all be squares?

Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org