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Dinh Tuan HUYNH 博士后：On the set of divisors with zero geometric defect

本站小编 Free考研/2020-05-19


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: Dinh Tuan HUYNH 博士后，中科院数学所
Inviter:
Title:
 On the set of divisors with zero geometric defect
Time & Venue:
 2020.01.07 10:10-11:40 N224
Abstract:
 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).

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