Quantum K-theory of Incidence Varieties

Abstract: Certain rational enumerative geometry problems can be formulated as intersection theory in the moduli space of stable maps M̅_{0,m}(X,d). This moduli space is well-behaved when $X$ is a projective homogeneous variety $G/P$. Non-trivial relations among solutions to these enumerative geometry problems (Gromov-Witten invariants) enable the definition of an associative product and in turn a formal deformation of the cohomology ring called the quantum cohomology ring of $X$. Similarly, a deformation of the Grothendieck ring $K(X)$ called the quantum K-theory ring of $X$ is defined using sheaf-theoretic versions of Gromov-Witten invariants.

After introducing relevant background, we will focus on the quantum K-theory of the projective homogeneous variety $Fl(1,n-1;n)$ (also called an incidence variety), where I have found explicit multiplication formulae and computed some sheaf-theoretic Gromov-Witten invariants. These computations lead to suspected rationality properties of some natural subvarieties of M̅_{0,m}(X,d).

algebraic geometry

Audience: researchers in the discipline

American Graduate Student Algebraic Geometry Seminar

Series comments: The American Graduate Student Algebraic Geometry Seminar (AGSAGS) is a virtual seminar by and for algebraic geometry graduate students.

The goal of this seminar is for graduate students to share their research through online talks and to provide an algebraic geometry graduate networking system. Grad students, postdocs, and professors are welcome to attend.

Seminars will be held on Mondays at 4 p.m. Eastern on Zoom. We hope this time is convenient for graduate students in the Americas, hence the name AGSAGS. Prior registration is required and interested participants should register here: sites.google.com/view/agsags/registration. In addition to graduate talks, there will be occasional social events.