The Local Structure of the Generic Theta Divisor

Explore a mathematical lecture that delves into a groundbreaking principle in deformation theory with cohomology constraints in characteristic zero, developed in collaboration with B. Wang and M. Rubio. Learn how this principle, which extends Deligne's deformation theory, is formulated using differential graded Lie modules and L-infinity modules. Discover how this theoretical framework has not only illuminated complex moduli spaces but also yielded a remarkable insight into classical algebraic geometry: for a generic compact Riemann surface, the theta function at every point on the Jacobian can be reduced to its first Taylor term through local holomorphic coordinate changes and unit multiplication.