Hyperelliptic Curves: Construction and Properties

• Standard quadratic models, simplified models
• Integral model, minimal Weierstrass model, p-normal model, reduced model
• Invariants: degree, genus, discriminant
• Function field of the curve
• Extension and lifting of curves induced by maps of base rings
• Reduction types and conductors of a genus 2 curve at odd primes
• Igusa and related invariants
• Construction of a curve given its Igusa invariants
• Determination of points at infinity