Computer Aided Algebraic Geometry

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Quasi-étale quotients Computer Aided Algebraic Geometry R. Pignatelli Surfaces Invariants Quasi-étale quotients Definitions Computing invariants Computer Calculations The Algorithms Classification Results Open Problems Definition A quasi-étale surface is the min. res. S of the sings of X = (C 1 × C 2 )/G where C i are Riemann Surfaces of genus g i ≥ 2 and G is a group of automorphisms acting freely out of a finite set of points. If π : C 1 × C 2 → X is the quotient map, we are assuming π quasi-étale (instead of étale). • What we lose: X is singular, we need to consider a resolution of its singularities S. 8 / 19
Quasi-étale quotients Computer Aided Algebraic Geometry R. Pignatelli Surfaces Invariants Quasi-étale quotients Definitions Computing invariants Computer Calculations The Algorithms Classification Results Open Problems Definition A quasi-étale surface is the min. res. S of the sings of X = (C 1 × C 2 )/G where C i are Riemann Surfaces of genus g i ≥ 2 and G is a group of automorphisms acting freely out of a finite set of points. If π : C 1 × C 2 → X is the quotient map, we are assuming π quasi-étale (instead of étale). • What we lose: X is singular, we need to consider a resolution of its singularities S. • What we gain: It may be K 2 < 8χ. We may in principle fill most of the picture. 8 / 19
Page 1 and 2: Computer Aided Algebraic Geometry R
Page 3 and 4: Birational Invariants Computer Aide
Page 9 and 10: Surfaces of general type Computer A
Page 11 and 12: Surfaces of general type Computer A
Page 13 and 14: M. Noether conjecture Computer Aide
Page 15 and 16: M. Noether conjecture Computer Aide
Page 17 and 18: Inequalities for surfaces of genera
Page 19 and 20: Beauville construction Computer Aid
Page 21 and 22: Quasi-étale quotients Computer Aid
Page 23: Quasi-étale quotients Computer Aid
Page 27 and 28: Mixed and unmixed structures Comput
Page 33 and 34: Constructing curves with group acti
Page 35 and 36: Constructing curves with group acti
Page 37 and 38: The irregularity Computer Aided Alg
Page 39 and 40: The irregularity Computer Aided Alg
Page 41 and 42: 13 / 19 K 2 and χ Computer Aided A
Page 43 and 44: The algorithms Computer Aided Algeb
Page 49 and 50: 15 / 19 Computer Aided Algebraic Ge
Page 57 and 58: Algorithmic problems Computer Aided
Page 59 and 60: Theoretical problems Computer Aided
Page 61: Literature Computer Aided Algebraic

Computer Aided Algebraic Geometry

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