Title：Some problems related to abundance for for 3-fold in char p 

 

Spearker： 张磊（陕西师范大学）

 

Time: 3月13日(周一), 9:00-10:30

Room：1208 

Abstract：Recently, Birkar, Hacon and Xu have proved existence of minimal model of 3-folds in char p >5. We focus on abundance 3-folds in char p >5: for a minimal klt 3-fold X, is the canonical divisor K_X semi-ample? According to whether X has non-trivial Albanese maps or not, we fall into two cases. Some progresses have been made for those varieties with non-trival Albanese maps in the recent years. In this case to prove abundance it suffices to prove (1) characterization of abelian varieties by the condition Kodaira dimension =0, that is, if a variety X has maximal Albanese dimension and Kodaira dimension zero, is X birational to an abelian variety. (2) Iitaka conjecture: for a fibration f: X ---> Y of smooth varieties, it is conjectured thatk(X) >= k(Y) + k(F) where F denotes the generic fiber. We will discuss the two problems. Very little is known for varieities with trival Albanese maps, if time permitting we will discuss this case and explain the main obstacles in this case.

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