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We construct the extension of a hyperelliptic K3 surface to a Fano $6$-fold with extraordinary properties in moduli. This leads us to a family of surfaces of general type with $p_g=1$, $q=0$, $K^2=2$ and hyperelliptic canonical curve, each of which is a weighted complete intersection inside a Fano $6$-fold. Finally, we use these hyperelliptic surfaces to determine an $8$-parameter family of Godeaux surfaces with $\pi_1=\ZZ/2$.
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참고문헌 (12)
참고문헌 신청
R. Barlow / 1984 / Some new surfaces with pg = 0 / Duke Math. J 51(4):889~904
R. Barlow / 1985 / A simply connected surface of general type with pg = 0 / Invent. Math 79(2):293~301
F. Catanese / 1989 / Surfaces with K2 = 2, pg = 1, q = 0 / J. Reine. Angew. Math 395:1~55
S. Coughlan / 2009 / Key varieties for surfaces of general type
S. Coughlan / 2014 / Extending symmetric determinantal quartic surfaces / Geom. Dedicata 172:155~177
R. Barlow / 1985 / A simply connected surface of general type with pg = 0 / Invent. Math 79(2):293~301
F. Catanese / 1989 / Surfaces with K2 = 2, pg = 1, q = 0 / J. Reine. Angew. Math 395:1~55
S. Coughlan / 2009 / Key varieties for surfaces of general type
S. Coughlan / 2014 / Extending symmetric determinantal quartic surfaces / Geom. Dedicata 172:155~177
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