Algebraic Geometry and Number Theory

  1. Aree Scientifiche
  2. Algebraic Geometry and Number Theory

Research interests

  • Birational geometry, classification of algebraic varieties and of their degenerations.
  • Minimal model program.
  • Algebraic curves, their families and their moduli.
  • Jacobians and abelian varieties.
  • Geometry of embeddings in projective spaces.
  • Algebraic surfaces and their moduli.
  • Moduli spaces of stable vector bundles on curves and Brill-Noether theory.
  • Moduli spaces of stable maps, virtual classes, Gromov-Witten invariants.
  • Moduli spaces of sheaves on K3 surfaces.
  • Hyperkaehler manifolds.
  • Ulrich bundles and their moduli spaces.
  • Holomorphic dynamics, residues, hyperbolicity.
  • Elliptic curve cryptography and post-quantum cryptography, isogeny based cryptography and isogeny graphs
  • Abelian varieties over number fields.
  • Algebraic curves over finite fields.
  • Arithmetic properties of algebraic varieties.
  • Arakelov class groups.
  • Group schemes.

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