Algebraic Geometry Seminar

Title

Twelve points on the projective line. Abstract: There are many ways to geometrically define a (PGL(2)-invariant) divisor in the variety of "12 points in P^1", Sym^{12}(P^1), isomorphic to P^{12}. For example: the 12 nodal cubics in a pencil of plane cubics; the branch points of a degree 4 map of a genus 3 hyperelliptic curve to P^1; the branch points of a genus 3 curve mapped to P^1 by the canonical sheaf; the branch points of a genus 4 curve mapped to P^1 by a theta-characteristic. We'll see that these divisors (and others) are all the same, by showing that the corresponding moduli spaces are covers of others. The links involve various beautiful classical constructions.

Abstract