Date:
Mon, 13/11/202314:30-16:00
Location:
Ross 70
Zoom link
https://huji.zoom.us/j/88037279712?pwd=N3MwWW5RYzRTZHg4K0U2bS80Rmxjdz09
Meeting ID: 880 3727 9712
Passcode: 955263
------------------------------------------------------------------------------------------------------
Title: Ceresa cycles of bielliptic Picard curves
Abstract: Let (C,o) be a pointed genus g curve. C embeds in its Jacobian J in two ways: C+ = {x-o : x in C} and C- = {o-x : x in C}. The Ceresa class is the difference [C+] - [C-] in the Chow group of 1-cycles on J. Ceresa proved that a very general curve of genus g has non-zero Ceresa cycle, showing that C+ and C- are (in general) not rationally equivalent. It was speculated that non-hyperelliptic curves have non-torsion Ceresa cycles. We show that the genus 3 curve y^3 = x^4 + ax^2 + b has torsion Ceresa cycle if and only if the point (a^2-4b, a(a^2 - 4b)) is a torsion point on the elliptic curve y^2 = x^3 + 4b(a^2 - 4b)^2. This gives infinitely many examples of torsion Ceresa cycle among genus three plane curves and implies a Northcott property for their height. This is joint work with Jef Laga.
https://huji.zoom.us/j/88037279712?pwd=N3MwWW5RYzRTZHg4K0U2bS80Rmxjdz09
Meeting ID: 880 3727 9712
Passcode: 955263
------------------------------------------------------------------------------------------------------
Title: Ceresa cycles of bielliptic Picard curves
Abstract: Let (C,o) be a pointed genus g curve. C embeds in its Jacobian J in two ways: C+ = {x-o : x in C} and C- = {o-x : x in C}. The Ceresa class is the difference [C+] - [C-] in the Chow group of 1-cycles on J. Ceresa proved that a very general curve of genus g has non-zero Ceresa cycle, showing that C+ and C- are (in general) not rationally equivalent. It was speculated that non-hyperelliptic curves have non-torsion Ceresa cycles. We show that the genus 3 curve y^3 = x^4 + ax^2 + b has torsion Ceresa cycle if and only if the point (a^2-4b, a(a^2 - 4b)) is a torsion point on the elliptic curve y^2 = x^3 + 4b(a^2 - 4b)^2. This gives infinitely many examples of torsion Ceresa cycle among genus three plane curves and implies a Northcott property for their height. This is joint work with Jef Laga.