ON A FIBER SPACE OVER A CURVE

  • 발행 : 1997.07.01

초록

Let X be a smooth projective threefold. Let C be a smooth projective curve and let $f : X \to C$ be a fiber space with connected fiber S. Assume that $q_1(S) = 0$. Then we have $-X(O_C)X(O_S) \leq -X(O_X)$.

키워드

참고문헌

  1. Algebraic Geometry R. Hartshorne
  2. Adv. Stud. in Pure Math v.1 Hodge theory and Kodaira dimension, Algebraic varieties and analytic varieties Y. Kawamata;S. Iitaka(ed.)
  3. Ann. of Math. v.123 Higher direct images of dualizing sheaves Ⅰ Y. Kollar
  4. Complex analysis and algebraic geometry Kodaira dimensions for certain fiber spaces K. Ueno;M. Nagata(ed.)