Download Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a by Enrico Arbarello, Corrado De Concini (auth.), Eduard PDF

By Enrico Arbarello, Corrado De Concini (auth.), Eduard Casas-Alvero, Gerald Welters, Sebastian Xambó-Descamps (eds.)

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Extra resources for Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a Conference held in Sitges (Barcelona), Spain October 5–12, 1983

Example text

Y Equiva- with Wl (x) = Kx ~ is ~2 K0x 2 but = Ox . All Enriques surfaces are algebraic. Examples of such of P3 acting on describe here the duce Y and o quartics because coordinates be a bihomogeneous polynomial i. (There is a one 13-dimensional 2, there is a double cover surface Y is the of bidegree vector space P1 x P1 intro- involution i: of such if P1 4,4 and invariant f). One m a y even does not pass through As the divisor class of R is divisible by ~: Y----+ P1 x P1 smooth and R = { f=O} c P1 x of the four fixed points.

Y. on X. all of P AssociaB y miX. 3). defined In o u r c a s e , through curve (cf. always obtained resp. Euler's Q X E - F = 2. P, follows: P xQ the is of the the divisor class in Px Q 3F+E, residual form IF[ T has In [Br i] l e n t with the Its degree with the is IFI planes computed cut out b y t h e p l a n e s bidegree (3,1) and X + P x Q P and P+TpQ(P) as through Segre also shows on X has b l o w s down some c u r v e s . Q. So = 3 d e g F + d e g E - deg P - 4 = transforms, of t h e F e r m a t q u a r t i c IEI, IE[.

I n : Complex Analysis & Algebraic Geometry, C a m b r i d g e (1977), 119-136. T. Every-K3 s u r f a c e is k~ihler Inv. Math. 37 139-150 (1983) St Sterk, H. To appear Todorov, A. Applications of the K~hler-Einstein-Calabi-Yau of K3-surfaces. Inv. Math. 81, 251-266 (1980) Ueno, K. On the K u m m e r Preprint Ve Univ. metric to surface associated with a curve of genus 2. Verra, A. B. The two most algebraic K3-surfaces Math. Ann. 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.

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