Pseudoeffective Cones and Morphisms of Projective Varieties

The cycles on an algebraic variety contain a great deal of information about its geometry. This thesis is concerned with the pseudoeffective cone obtained by taking the closure of the cone of numerical classes of effective cycles on algebraic varieties. Our interest, motivated by different existing lines of research, is in showing when the pseudoeffective cone is not polyhedral in specific examples. We do this by first proving a sufficient criterion for non-polyhedral pseudoeffective cone (also known as Mori cone) for the case of surfaces. We apply this to the case of C x C where C is a smooth curve of genus at least 2. Using induction, we prove that all intermediate cones of cycles on C x ... x C are not polyhedral. Finally, we study the case of surfaces fibered over curve and give a sufficient criterion for when its pseudoeffective cone is not polyhedral.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146074/1/ashwathr_1.pd