諾特線上(2,4)-型之三維代數多樣體

Abstract

本文具體地構造出數個 (2, 4)-型的三維代數多樣體的例子，並描述它們的極小模型 (minimal model) 與正則模型 (canonical model)；這些代數多樣體落在諾特線 (Noether line) 上。對於每個例子 X，我們也計算了上同調空間 H^1(X, T_X) 的維度；該空間描述了 X 的一階形變。這推廣了堀川穎二 (E. Horikawa) 在曲面 (即二維情形) 上的一部份工作。

We construct explicit examples of algebraic threefolds of general type with invariants (vol(X), p_g(X)) = (2, 4) and describe their minimal and canonical model(s); in particular, such threefolds lie on the Noether line. For each of the examples X, we compute the dimension of H^1(X, T_X), the space of first-order infinitesimal deformations of X; this partially generalizes E. Horikawa’s work on surfaces.