AbstractA general curve C of genus 6 can be embedded into the unique quintic del Pezzo surface X_5 as a divisor of class -2K_{X_5}. This embedding is unique up to the action of the symmetric group S_5. Taking a double cover of X_5 branched along C yields a K3 surface Y. Thus the K-moduli spaces of the pair (X_5, cC) can be studied via wall-crossing and by relating them to the Hassett-Keel progr...
AbstractWe briefly review the origin in physics of attractor points on the moduli space of Calabi-Yau threefolds. We turn to their mathematical interpretation as special cases of Hodge loci. This leads to fascinating conjectures on the modularity of the Calabi-Yau threefolds at these points in terms of their periods and L-functions. For hypergeometric one-parameter families of Calabi-Yau threef...