Extremal contractions of 2-Fano fourfolds
Florian Schrack
TL;DR
This paper investigates extremal contractions on smooth Fano fourfolds with positive second Chern character, establishing restrictions on the types of contractions possible.
Contribution
It proves that extremal contractions on such fourfolds cannot be of fiber type nor contract a divisor to a point, providing new classification constraints.
Findings
Contractions cannot be of fiber type.
Divisorial contractions to a point are impossible.
Results restrict the structure of 2-Fano fourfolds.
Abstract
We consider extremal contractions on smooth Fano fourfolds whose second Chern character is positive. We show that such contractions can neither be of fiber type nor contract a divisor to a point.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology