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Niveau: Supérieur, Doctorat, Bac+8

TODAY'S MENU: GEOMETRY AND RESOLUTION OF SINGULAR ALGEBRAIC SURFACES E. FABER AND H. HAUSER Abstract. The courses are: Triviality, Tangency, Transversality, Symmetry, Simplicity, Singularity. These characteristic local plates serve as our invitation to algebraic surfaces and their resolution. Please take a seat. Contents Appetizers 1 Ingredients 4 Triviality: Whitney Umbrella x2 = y2z 9 Tangency: Kolibri y2 = x2z2 + x3 13 Transversality: Iris x2y + y2z = z4 16 Symmetry: Helix x4 + y2z2 = x2 19 Simplicity: Sofa x2 + y3 + z5 = 0 24 Singularity: Daisy (x2 ? y3)2 = (z2 ? y2)3 32 Appendix: Basic concepts 36 References 39 Our menu consists of six geometric phenomena related to the resolution of singularities of algebraic surfaces. The courses are Triviality (soup), Tangency (salad), Transversality (fish), Symmetry (roast), Simplicity (dessert) and Singularity (digestif). In each course a selected singular surface will illustrate these concepts. On the way, we will resolve the surface and depict its resolution process graphically. After some appetizers we present the basic ingredients of our dinner. For the cooking we will mostly use algebraic food. To keep the appetite alive, the more technical definitions (of singularities, blowups, resolution, normal crossings, . . .

TODAY'S MENU: GEOMETRY AND RESOLUTION OF SINGULAR ALGEBRAIC SURFACES E. FABER AND H. HAUSER Abstract. The courses are: Triviality, Tangency, Transversality, Symmetry, Simplicity, Singularity. These characteristic local plates serve as our invitation to algebraic surfaces and their resolution. Please take a seat. Contents Appetizers 1 Ingredients 4 Triviality: Whitney Umbrella x2 = y2z 9 Tangency: Kolibri y2 = x2z2 + x3 13 Transversality: Iris x2y + y2z = z4 16 Symmetry: Helix x4 + y2z2 = x2 19 Simplicity: Sofa x2 + y3 + z5 = 0 24 Singularity: Daisy (x2 ? y3)2 = (z2 ? y2)3 32 Appendix: Basic concepts 36 References 39 Our menu consists of six geometric phenomena related to the resolution of singularities of algebraic surfaces. The courses are Triviality (soup), Tangency (salad), Transversality (fish), Symmetry (roast), Simplicity (dessert) and Singularity (digestif). In each course a selected singular surface will illustrate these concepts. On the way, we will resolve the surface and depict its resolution process graphically. After some appetizers we present the basic ingredients of our dinner. For the cooking we will mostly use algebraic food. To keep the appetite alive, the more technical definitions (of singularities, blowups, resolution, normal crossings, . . .

- arbitrarily given curve
- singular algebraic
- twin-points
- locally analytically
- characteristic there
- most singular
- local geometry

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Published by | mijec |

Reads | 13 |

Language | English |

Document size | 3 MB |

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