PICARD LATTICES OF FAMILIES OF K3 SURFACES

REFERENCES

• Batyrev , V.V. 1994 . Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties . J. Algebraic Geom. , 3 ( 3 ) : 493 – 535 .
   Google Scholar
• Barth , W. , Peters , C. and Van de Ven , A. 1984 . Compact Complex Surfaces, Ergebnisse den Mathematik, 3. Folge, Band 4 Berlin : Springer-Verlag .
   Google Scholar
• Belcastro , S-M. Picard Lattices of Families of K3 Surfaces University of Michigan Ph.D. dissertation, 1997. Available also for download at http://www.math.uni.edu/˜smbelcas/prof.html
   Google Scholar
• Brieskorn , E. 1983 . The Milnor Lattices of the Exceptional Unimodular Singularities Vol. 150 , Bonner Mathematische Schriften .
   Google Scholar
• Cox , D.A. 1989 . Picard Numbers of Surfaces in 3-Dimensional Weighted Projective Spaces . Math. Z. , 201 : 183 – 189 .
   Web of Science ®Google Scholar
• Danilov , V.I. 1978 . The Geometry of Toric Varieties . Russian Math. Surveys , 33 ( 2 ) : 97 – 154 .
   Google Scholar
• Dolgachev , I.V. 1996 . Mirror Symmetry for Lattice Polarized K3 Surfaces, Algebraic Geometry, 4 . J. Math. Sci. , 81 ( 3 ) : 2599 – 2630 .
   Google Scholar
• — . 1982 . Weighted Projective Varieties Vol. 956 , 34 – 72 . New York : Springer-Verlag . in “Group Actions and Vector Fields,” Lect. Notes in Math
   Google Scholar
• Fulton , W. 1993 . Introduction to Toric Varieties, Annals of Mathematics Studies Princeton : Princeton University Press .
   Google Scholar
• Iskovskikh , V.A. and Shafarevich , I.R. 1996 . “ Algebraic Surfaces ” . In Algebraic Geometry II, Encyclopaedia of Math. Sci. Vol. 35 , 127 – 262 . New York : Springer-Verlag .
   Google Scholar
• Khovanskiĭ , A.G. 1977 . Newton Polyhedra and Toroidal Varieties . Funct. Anal. App. , 11 : 289 – 296 .
   Google Scholar
• Khovanskiĭ , A.G. 1984 . Newton Polyhedra (Resolution of Singularities) . J. Soviet Math. , 27 : 2811 – 2830 .
   Google Scholar
• Kreuzer , M. and Skarke , H. 1998 . Classification of Reflexive Polyhedra in Three Dimensions . Adv. Theor. Math. Phys. , 2 ( 4 ) : 853 – 871 .
   Google Scholar
• Miranda , R. The Basic Theory of Elliptic Surfaces ETS Editrice Pisa, ISBN 88-7741-462
   Google Scholar
• Nikulin , V.V. 1980 . Integral Symmetric Bilinear Forms and Some of their Applications . Math. USSR-Izv. , 14 ( 1 ) : 103 – 167 .
   Web of Science ®Google Scholar
• Shioda , T. 1972 . On Elliptic Modular Surfaces . J. Math. Soc. Japan , 24 : 20 – 59 .
   Web of Science ®Google Scholar
• Yonemura , T. 1990 . Hypersurface K3 Singularities . Tôhoku Math J. , 42 : 351 – 380 .
   Web of Science ®Google Scholar
• While Batyrev's mirror construction does not always give the correct K3 mirror (see [7]), the spirit of his work suggests that Kreuzer/Skarke's 4319 toric K3 hypersurfaces [13] will mirror each other; the author is currently working to confirm this.)
   Google Scholar