5 citations · 13 across the 14 of their papers we have counts for
16 papers
Varieties of minimal degree in weighted projective space
Maya Banks, Ritvik Ramkumar
We initiate a study of varieties of minimal degree in weighted projective spaces. We call a weighted projective space divisible if fo…
Projectivity of the moduli of equidimensional branchvarieties
Daniel Halpern-Leistner, Andres Fernandez Herrero, Trevor Jones +1
We resolve an open problem posed by Alexeev-Knutson on the projectivity of the moduli of branchvarieties in the equidimensional case. As an application, we construct projective mod…
Cartwright-Sturmfels Hilbert Schemes
Ritvik Ramkumar, Alessio Sammartano
Let S be the Cox ring of a product of r projective spaces. In this paper, we study the Cartwright-Sturmfels Hilbert schemes of S, which are multigraded Hilbert schemes that only pa…
The Hilbert scheme of points on a threefold: broken Gorenstein structures and linkage
Joachim Jelisiejew, Ritvik Ramkumar, Alessio Sammartano
We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees s…
On the parity conjecture for Hilbert schemes of points on threefolds
Ritvik Ramkumar, Alessio Sammartano
Let be the Hilbert scheme of points in , and let denote the tangent space to a point . Okounkov and Pandharipande have conjectured t…
On Rees algebras of 2-determinantal ideals
Ritvik Ramkumar, Alessio Sammartano
Let I be the ideal of minors of a 2 by n matrix of linear forms with the expected codimension. In this paper we prove that the Rees algebra of I and its special fiber ring are Cohe…
A local study of the fiber-full scheme
Yairon Cid-Ruiz, Ritvik Ramkumar
We study some of the local properties of the fiber-full scheme, which is a fine moduli space that generalizes the Hilbert scheme by parametrizing closed subschemes with prescribed…
Rational singularities of nested Hilbert schemes
Ritvik Ramkumar, Alessio Sammartano
The Hilbert scheme of points of a smooth surface is a well-studied parameter space, lying at the interface of algebraic geometry, commutative algebra, repr…
The fiber-full scheme
Yairon Cid-Ruiz, Ritvik Ramkumar
We introduce the fiber-full scheme which can be seen as the parameter space that generalizes the Hilbert and Quot schemes by controlling the entire cohomological data. The fiber-fu…
A Hilbert scheme of radius two
Ritvik Ramkumar
We give an explicit example of a Hilbert scheme whose incidence graph has radius two.
The Hilbert scheme of a pair of linear spaces is a Mori dream space
Ritvik Ramkumar
Let denote the component of the Hilbert scheme whose general point parameterizes an -plane union a -plane meeting transversely in . We describe the…
On the smoothness of lexicographic points on Hilbert schemes
Ritvik Ramkumar, Alessio Sammartano
We study the geometry of standard graded Hilbert schemes of polynomial rings and exterior algebras. Our investigation is motivated by a famous theorem of Reeves and Stillman for th…
On the tangent space to the Hilbert scheme of points in P3
Ritvik Ramkumar, Alessio Sammartano
In this paper we study the tangent space to the Hilbert scheme , motivated by Haiman's work on and by a long-standing c…
Hilbert schemes with two Borel-fixed points
Ritvik Ramkumar
We characterize Hilbert polynomials that give rise to Hilbert schemes with two Borel-fixed points and determine when the associated Hilbert schemes or their irreducible components…
The Hilbert scheme of a pair of linear spaces
Ritvik Ramkumar
Let denote the component of the Hilbert scheme whose general point parameterizes an -plane union a -plane meeting transversely in . We sho…
Embeddings of quotient division algebras of rings of differential operators
Jason P. Bell, Colin Ingalls, Ritvik Ramkumar
Let be an algebraically closed field of characteristic zero, let and be smooth irreducible algebraic curves over , and let and denote respectively the…