Birational geometry of terminal quartic 3-folds, I

The paper explores the birational geometry of terminal quartic 3-folds. In doing this I develop a new approach to study maximal singularities with positive dimensional centers. This allows to determine the pliability of a Q-factorial quartic with ordinary double points, and it shows the importance of Q-factoriality in the context of birational geometry of uniruled 3-folds

[1]  Nikolaos Tziolas,et al.  Terminal 3-fold Divisorial Contractions of a Surface to a Curve I , 2001, Compositio Mathematica.

[2]  M. Kawakita.  General elephants of three-fold divisorial contractions , 2002 .

[3]  M. Kawakita.  Divisorial Contractions in Dimension Three which Contract Divisors to Compound A1 Points , 2000, Compositio Mathematica.

[4]  Hari K. Kunduri,et al.  Homogeneous plane-wave spacetimes and their stability , 2003, gr-qc/0310013.

[5]  M. Kawakita.  General elements in anticanonical systems of threefolds with divisorial contractions and applications to classification , 2001, math/0110050.

[6]  M. Kawakita.  Divisorial contractions in dimension three which contract divisors to smooth points , 2000, math/0005207.

[7]  M. Grinenko.  Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2 , 2000, math/0002252.

[8]  Михаил Михайлович Гриненко,et al.  Бирациональные свойства пучков поверхностей дель Пеццо степеней 1 и 2. II@@@Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2. II , 2000 .

[9]  A. R. Iano-Fletcher,et al.  Explicit Birational Geometry of 3-Folds: Working with weighted complete intersections , 2000 .

[10]  Miles Reid,et al.  Explicit Birational Geometry of 3-Folds: Fano 3-fold hypersurfaces , 2000 .

[11]  M. Reid,et al.  Explicit birational geometry of 3-folds , 2000 .

[12]  A. Corti.  Explicit Birational Geometry of 3-Folds: Singularities of linear systems and 3-fold birational geometry , 2000 .

[13]  Miles Reid,et al.  Graded rings and birational geometry , 2000 .

[14]  A. Pukhlikov.  Explicit Birational Geometry of 3-Folds: Essentials of the method of maximal singularities , 2000 .

[15]  M. Grinenko.  Birational automorphisms of a three-dimensional double cone , 1998, math/9808132.

[16]  A. Pukhlikov.  Essentials of the method of maximal singularities , 1998, math/9806138.

[17]  Y. Kawamata.  Divisorial contractions to 3-dimensional terminal quotient singularities , 1996 .

[18]  D. Jaffe.  Applications of iterated curve blow-up to set theoretic complete intersections in 3. , 1994, alg-geom/9410008.

[19]  J. Kollár,et al.  Classification of three-dimensional flips , 1992 .

[20]  J. Kollár.  Flips and Abundance for Algebraic Threefolds , 1992 .

[21]  V. A. Iskovskikh.  DOUBLE PROJECTION FROM A LINE ON FANO THREEFOLDS OF THE FIRST KIND , 1990 .

[22]  A. Pukhlikov.  BIRATIONAL AUTOMORPHISMS OF A THREE-DIMENSIONAL QUARTIC WITH A QUADRATIC SINGULARITY , 1989 .

[23]  S. D. Cutkosky,et al.  Elementary contractions of Gorenstein threefolds , 1988 .

[24]  Y. Kawamata.  Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces , 1988 .

[25]  J. Kollár.  The structure of algebraic threefolds: an introduction to Mori's program , 1987 .

[26]  Miles Reid,et al.  Young person''s guide to canonical singularities , 1985 .

[27]  M. Reid.  Minimal Models of Canonical 3-Folds , 1983 .

[28]  K. Hulek.  The normal bundle of a curve on a quadric , 1981 .

[29]  Ju. Manin,et al.  THREE-DIMENSIONAL QUARTICS AND COUNTEREXAMPLES TO THE LÜROTH PROBLEM , 1971 .

[30]  V A Iskovskih,et al.  RATIONAL SURFACES WITH A PENCIL OF RATIONAL CURVES AND WITH POSITIVE SQUARE OF THE CANONICAL CLASS , 1970 .