Some Topics in Several Complex Variables

间：2020.1.7（星期二）, 8:30-10:00

点：数学院南楼N224

要：Recently, Dinh-Sibony introduced the notation of density currents associated to a family {Ti}qi=1 of finite positive closed currents on a compact K？hler manifold. In the case where the density current associated to {Ti}qi=1 is uniquely determined, it could be used to define a suitable wedge product of Ti. Thus the notation of density currents extends the theory of intersection for positive closed currents.  In this talk, we will report some main ideas in this fundamental work and discuss some of its application.

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间：2020.1.7（星期二）, 10:10-11:40

点：数学院南楼N224

要：Let f : C X be a transcendental holomorphic curve into a projective manifold X. Based on the recent theory of density currents by Dinh-Sibony, we show that given a very ample line bundle L, there is an exceptional set of divisors which is a countable union of proper algebraic subsets of the space of effective divisors generated by global sections of L such that for every divisor D outside this set, the geometric defect of D (i.e, the defect of truncation 1) with respect to f is zero. This result could be regarded as a generalization of the classical Casorati-Weierstrass Theorem, as well as a weak version of the fundamental conjecture for entire holomorphic curves into projective varieties in the case where the canonical line bundle is 0. This is a joint work with Duc-Viet Vu (K？ln).