Title: Enriques surfaces: fundamental polarizations and their mirror families

Abstract: Among algebraic surfaces, Enriques' locate between K3 and rational surfaces. Enriques' are not so familiar as K3's but as interesting as they. I first explain their 9 fundamental polarizations which correspond to 9 vertices of the E10 diagram. Each fundamental polarization has symmetry of the Weyl group of the complementary ADE diagram (of rank 9). It also determines the mirror, that is, a 1-dimensional family of Enriques surfaces characterized by such an ADE diagram in a certain way. I will give explicit equations and description of automorphism groups of the mirrors (with few exceptions).(6/6/16(F))

Section 1. Fundamental polarization
Section 2. Definition of "mirror families"
Section 3. Mirror (family) of w2
Section 4. Mirror (family) of w4
Section 5. Mirror (family) of Fano polarization w10