By Enrico Arbarello, Corrado De Concini (auth.), Eduard Casas-Alvero, Gerald Welters, Sebastian Xambó-Descamps (eds.)
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Additional info for Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a Conference held in Sitges (Barcelona), Spain October 5–12, 1983
Position. H°(C,L) 13 we can = 0 if proceed by L is the increasing n. D. We h a v e two e n t i r e l y P r o p o s i t i o n 20. L e t F a generic transversal a generic even to D even P r o o f . Let be n only a reduced invevtible and let invevtible of i n t e r s e c t i o n of We D analogous be D be degree the union of D even on D . of D G on and of let and C multidegree, Let Q. ,p2 n and a there conic exists G®O D - F(1). be t h e points Q. the u s e d i n t h e p r o o f of p r o p . cuvve thetachavactevistic C with We h a v e t h e e x a c t plane thetachavactevistic the sketch results.
By L e f s c h e t z ' And b y the theo- adjunction for- quartic does mula K S = KP3 ® because KP3 not contain lines. = 0P3(-~). any Finding S) and line. all describing So But and is special these lines and a K3-surface. quartics (which their incidences on a family of examples Let ~ S 0S(~) = 0 S, The usually are general have nodal a tendency curves is quite amusing. on to contain the This is n o w K3-surface demonstrated due to Segre [Se 3]. tp b e two h o m o g e n e o u s quartic polynomials i n two v a r i a b l e s consider f ( z o .
265, 1-21 (1983) surface. Press moduli GENERIC INVERTIBLE SHEAVES OF 2-TORSION AND GENERIC THETACHARACTERISTICS INVERTIBLE ON N O D A L P L A N E C U R V E S Frabrizio Catanese* I. D e f i n i t i o n 1. Let an invertible Definitions and D sheaf be on a D if the following condition statements reduced such plane that L2 ~ of t h e r e s u l t s curve of O D. L degree is n, said and L to b e g e n e r i c holds: (2) (here, as usual, Moreover L t i o n of D square is said i, then Definition are 3.
Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a Conference held in Sitges (Barcelona), Spain October 5–12, 1983 by Enrico Arbarello, Corrado De Concini (auth.), Eduard Casas-Alvero, Gerald Welters, Sebastian Xambó-Descamps (eds.)