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Algebraic Geometry: "Fano varieties where all pseudoeffective divisors are also numerically effective"

Dr. Wenhao Ou, UCLA

Thursday, February 16, 2017
  1:10–2 p.m.

Location: Surge Building 268
  Parking Information

Category: Seminar

Description: We recall that a divisor in a smooth projective variety is said to be numerically effective (or nef) if it meets each curve with non negative intersection number, and is called pseudoeffective if it is the limit of effective Q-divisor classes. Both of these properties are ways in which a divisor can be in some sense “positive”. A nef divisor is always pseudoeffective, but the converse is not true in general. A Fano varity is a special variety whose anti-canonical divisor is ample. From the Cone Theorem, it turns out that the geometry of a Fano variety is closely related to its nef divisors. In this talk, we will consider Fano varieties such that all pseudoeffective divisors are nef. Wisniewski shows that the Picard number of such a variety is at most equal to its dimension. Druel classifies these varieties when these two numbers are equal. We classify the case when the Picard number is equal to the dimension minus 1.

Additional Information: AG Seminar

Open to: General Public
Admission: Free
Sponsor: Mathematics

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