An example of a Teichmuller disk in genus 4 with degenerate   Kontsevich-Zorich spectrum
  We construct an orientable holomorphic quadratic differential on a Riemann surface of genus 4 whose SL(2,R)-orbit is closed and has a highly degenerate Kontsevich - Zorich spectrum. This example is related to a previous similar construction in genus 3 by the first author. 
Giovanni Forni and Carlos Matheus