Instructor: Ali
Sinan Sertöz, Department of Mathematics
Room: SA-121, Phone: 1490
Office Hours: Wednesday 10:40-12:30
Suplementary Texts:
Schedule:
WEDNESDAY | 8:40-10:30 | SAZ-21 |
FRIDAY | 10:40-12:30 | SAZ-21 |
Topics to discuss:
Bundles, sheaves, divisors
Chern classes
Curves on surfaces
Enriques Kodaira classification
Invariants of K3 surfaces
Moduli for K3
Surjectivity of the period map for K3
Invariants for Enriques surfaces
The period map for Enriques surfaces
Grading:
Each student will choose an article from the following list and give a
detailed presentation of it in class at the end of the semester and will
circulate a written version of that talk incorporating all the comments and
suggestions which arise during the presentation. The final grade will reflect
the combined success of the talk and its written report.
Here is the list of suggested articles:
Knutsen, Andreas Leopold; Smooth curves on projective
K3 surfaces
Math Scand 90 (2002) 215-231.
Kovacs, Sandor; The cone of curves on a K3 surface,
Math Ann 300 (1994) 681-691.
Keum, Jong Hae; Every algebraic Kummer surface is the
K3 cover of an Enriques surface
Nagoya Math J 118 (1990) 99-100.
Morrison, David; On K3 surfaces with large Picard
number,
Invent Math 75 (1984) 105-121.
Önsiper & Sertöz; Generalized Shioda-Inose
structures on K3 surfaces,
Manuscripta Math 98 (1999) 491-495.
Saint-Donat, B; Projective models of K3 surfaces,
Amer J Math 96 (1974) 602-639.
Sertöz; Which singular K3 surfaces cover an Enriques
surface,
Proc Amer Math Soc (2004).
Shioda & Inose; On singular K3 surfaces,
Complex Analysis and Algebraic Geometry, Edited by W. L. Baily, Jr., and T.
Shioda, (1977), pp119-136.
Presentations:
Caner Koca,
Title: On K3 surfaces with large Picard
number,
Date: 10-12 November, 2004
Süleyman Tek,
Title: 2-Geometries and the Hamilton-Jacobi equation, (Garcia-Godines
et al, J Math Phys, 45 (2004) 725-735.)
Date: 8-10 December, 2004
Sultan Erdoğan,
Title: Every algebraic Kummer surface is the
K3 cover of an Enriques surface
Date: 15-17 December, 2004
Mesut Şahin
Title: Which singular K3 surfaces cover an Enriques
surface,
Date: 22-24 December, 2004
İnan Utku Türkmen,
Title: Families of K3 surfaces, (Mayer, Nagoya Math J, 48 (1972)
1-17.)
Date: 29-31 December, 2004
Vector bundles, Picard group, divisors, sections of bundles, building new bundles and obtaining their transition functions from the original ones
Connection, curvature, Chern-Weil theory
Zeros of sections and relation to Chern classes, Gauss-Bonnet
Borel & Serre, Le Theoreme de Riemann-Roch, Bull. Soc. math. France, 86 (1958), 97-136.
Grothendieck, La theorie des classes de Chern, Bull. Soc. math. France, 86 (1958), 136-154.
K3 surfaces
Barth & Hulek & Peters & Van De Ven, Compact Complex Surfaces, Springer, Second enlarged edition (2004), chapter VIII, K3 surfaces and Enriques surfaces
Miles Reid, Chapters on Surfaces,Complex
algebraic geometry (Park City, UT, 1993), 3--159,
IAS/Park City Math. Ser., 3, Amer. Math. Soc., Providence, RI, 1997, chapter
3, K3's.
Surjectivity of the period map for K3 surfaces
Namikawa, Surjectivity of period map for K3 surfaces, Katata Symposium 1982, Ed: Ueno, Progress in Math, Birkhauser, Vol 139, (1983), 379-397.
Looijenga, A Torelli theorem for Kahler-Einstein K3 surfaces, LNM 894, Springer-Verlag, (1981), 107-112.
Siu, A simple proof of the surjectivity of the period map of K3 surfaces, Manuscripta Math., 35 (1981), 311-321.
Cone of Curves on a K3
Kovacs, The cone of curves on a K3 surface, Math Ann 300 (1994) 681-691.
Clemens & Kollar & Mori, Higher Dimensional Complex Geometry, Asterisque, Vol 166 (1988), lecture 4, the cone of curves-the smooth case, pp22-27.
Son güncelleme: 19 Şubat 2005 Cumartesi