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Combinatorial Models for the Variety of Complete Quadrics
Soumya Banerjee, Mahir Bilen Can, Michael Joyce
We develop several combinatorial models that are useful in the study of the -variety of complete quadrics. Barred permutations parameterize the fixed points of…
Wonderful Symmetric Varieties and Schubert Polynomials
Mahir Bilen Can, Michael Joyce, Benjamin Wyser
Extending results of Wyser, we determine formulas for the equivariant cohomology classes of closed orbits of certain families of spherical subgroups of on the flag variety $…
Landen transforms as families of (commuting) rational self-maps of projective space
Michael Joyce, Shu Kawaguchi, Joseph H. Silverman
The classical (m,k)-Landen transform F_{m,k} is a self-map of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m'th…
SL(2)-regular Subvarieties of Complete Quadrics
Mahir Bilen Can, Michael Joyce
We determine SL(n)-stable, SL(2)-regular subvarieties of the variety of complete quadrics. We extend the results of Akyıldız and Carrell on Kostant-Macdonald identity by computing…
Regular Unipotent Invariants on the Wonderful Compactification of Complete Binary Forms
Mahir Bilen Can, Roger Howe, Michael Joyce
We investigate the topology of the closure in a wonderful compactification of the set of unipotent-invariant bilinear forms.
Unipotent Invariant Matrices
Mahir Bilen Can, Roger Howe, Michael Joyce
We describe the variety of fixed points of a unipotent operator acting on the space of matrices. We compute the determinant and the rank of a generic (symmetric, or anti-symmetric)…
The nef cone volume of generalized Del Pezzo surfaces
Ulrich Derenthal, Michael Joyce, Zach Teitler
We compute a naturally defined measure of the size of the nef cone of a Del Pezzo surface. The resulting number appears in a conjecture of Manin on the asymptotic behavior of the n…