Seminari del Dipartimento di Matematica

Seminario del 2023

Shigeyuki Kondo

Around Kummer surfaces II

nel ciclo di seminari: PROGETTO STRUTTURE: SHAPES, SYMMETRIES AND ARRANGEMENTS

algebra e geometria

Part 2: Quadratic line complexes and Kummer surfaces. A quadratic line complex is a nonsingular 3-fold which is the intersection of the Grassmannian G(1,3) (= lines in P^3) and a quadric in P^5. It naturally gives us a Kummer quartic surface S with 16 nodes, a curve C of genus 2, and an abelian surface A. Then A is isomorphic to the Jacobian of C and S is the quotient of A by its inversion. We give a sketch of this classical theory and extend the theory to the case of characteristic 2. Main references are Griffiths, Harris, Principles of Algebraic Geometry, the last chapter and T. Katsura, S. Kondo, arXiv:2301.01450.