Assistant Professor, Mathematics and Computer Science
Julia Rogers 139
Ph.D. in Mathematics, Johns Hopkins University, 2011
Areas of Scholarly Expertise and Interest
Joe Cutrone's research is in higher dimensional birational algebraic geometry.
His current research is in the classification of smooth weak Fano complex projective threefold varieties. These are varieties whose anticanonical divisor is nef and big, but not ample. He is particularly interested in weak Fano varieties with Picard number two whose Mori extremal contraction is divisorial (Type E). These varieties play a central role in a branch of Algebraic Geometry called Sarkisov Theory, which falls under the general umbrella of the Mori Minimal Model Program.
On the existence of certain weak Fano threefolds of Picard number two, co-authored with N. Marshburn and M. Arap.
This is a continuation in the study of weak Fano threefolds started in my thesis. We construct smooth weak Fano threefolds of Picard number two with small anti-canonical map obtained by blowing up certain curves on a smooth quadric in P4 and on smooth del Pezzo threefolds of degrees 4 and 5. In addition, we give the construction of weak Fano threefolds with small anti-canonical map arising as blow-ups of prime Fano threefolds X10, X16 and X18 along twisted cubics.
Towards the Classification of Weak Fano Threefolds with p=2, co-authored with N. Marshburn. (submitted)
This is a step towards finishing the classification of complex projective smooth weak Fano threefolds with Picard number two. I focus on the varieties that give examples of Sarkisov links of type II. These varieties have a divisorial extremal contraction (type E) and their pluri-anticanonical morphism contracts only a finite number of curves. The numerical existence of these varieties is completed. The geometric realization of these varieties is an ongoing project.