tailieunhanh - Đề tài " Quasi-projectivity of moduli spaces of polarized varieties "
By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of nonuniruled polarized varieties. Contents Introduction Singular hermitian metrics Deformation theory of framed manifolds; V -structures Cyclic coverings Canonically polarized framed manifolds Singular Hermitian metrics for families of canonically polarized framed manifolds 7. | Annals of Mathematics Quasi-projectivity of moduli spaces of polarized varieties By Georg Schumacher and Hajime Tsuji Annals of Mathematics 159 2004 597 639 Quasi-projectivity of moduli spaces of polarized varieties By Georg Schumacher and Hajime Tsuji Dedicated to our wives Rita and Akiko Abstract By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of nonuniruled polarized varieties. Contents 1. Introduction 2. Singular hermitian metrics 3. Deformation theory of framed manifolds V-structures 4. Cyclic coverings 5. Canonically polarized framed manifolds 6. Singular Hermitian metrics for families of canonically polarized framed manifolds 7. The convergence property of generalized Petersson-Weil metrics 8. Moduli spaces of framed manifolds 9. Fiber integrals and determinant line bundles for morphisms 10. L2-methods 11. Multiplier ideal sheaves 12. A criterion for quasi-projectivity 13. Bigness of L and the weak embedding property 14. Embedding of nonreduced spaces 15. Proof of the quasi-projectivity criterion References 1. Introduction In algebraic geometry it is fundamental to study the moduli spaces of algebraic varieties. As for the existence of moduli spaces it had been known that there exists an algebraic space as a coarse moduli space of nonuniruled polar 598 GEORG SCHUMACHER AND HAJIME TSUJI ized projective manifolds with a given Hilbert polynomial. Here an algebraic space denotes a space which is locally a finite quotient of an algebraic variety. Actually the notion of algebraic spaces was introduced to describe the moduli spaces AR1 . According to the theory of algebraic spaces by M. Artin AR1 AR2 KT the category of proper algebraic spaces of finite type defined over C is equivalent to the category of Moishezon spaces. Hence the moduli spaces of nonuniruled polarized manifolds have abundant meromorphic functions and were .
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