Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Ramkumar, Ritvik"'
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 smoothness on the Hilbert scheme. Moreover, we conjecture that it is ex
Externí odkaz:
http://arxiv.org/abs/2409.17009
Autor:
Ramkumar, Ritvik, Sammartano, Alessio
Let $Hilb^d(A^3)$ be the Hilbert scheme of $d$ points in $A^3$, and let $T_z$ denote the tangent space to a point $z \in Hilb^d(A^3)$. Okounkov and Pandharipande have conjectured that $\dim T_z$ and $d$ have the same parity for every $z$. For points
Externí odkaz:
http://arxiv.org/abs/2302.02204
Autor:
Ramkumar, Ritvik, Sammartano, Alessio
Publikováno v:
Journal of the London Mathematical Society 109, e12821 (2024)
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 Cohen-Macaulay and Koszul; in particular, they are quadratic algebras. The
Externí odkaz:
http://arxiv.org/abs/2210.12668
Autor:
Cid-Ruiz, Yairon, Ramkumar, Ritvik
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 cohomological data. As a consequence, we provide sufficient conditions
Externí odkaz:
http://arxiv.org/abs/2202.06652
Autor:
Ramkumar, Ritvik, Sammartano, Alessio
Publikováno v:
International Mathematics Research Notices 2024, 1061-1122
The Hilbert scheme of points $\mathrm{Hilb}^n(S)$ of a smooth surface $S$ is a well-studied parameter space, lying at the interface of algebraic geometry, commutative algebra, representation theory, combinatorics, and mathematical physics. The founda
Externí odkaz:
http://arxiv.org/abs/2109.09002
Autor:
Cid-Ruiz, Yairon, Ramkumar, Ritvik
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-full scheme $\text{Fib}_{\mathcal{F}/X/S}^\mathbf{h}$ is a fine moduli s
Externí odkaz:
http://arxiv.org/abs/2108.13986
Autor:
Ramkumar, Ritvik
We give an explicit example of a Hilbert scheme whose incidence graph has radius two.
Comment: 4 pages, 1 figure
Comment: 4 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2008.11968
Autor:
Ramkumar, Ritvik
Let $H_{a,b}^n$ denote the component of the Hilbert scheme whose general point parameterizes an $a$-plane union a $b$-plane meeting transversely in $\mathbf{P}^n$. We describe the effective and nef cones of $H_{a,b}^n$ and determine when the componen
Externí odkaz:
http://arxiv.org/abs/2006.06211
Autor:
Ramkumar, Ritvik, Sammartano, Alessio
Publikováno v:
Journal of Pure and Applied Algebra, Volume 226, Issue 3, March 2022, 106872
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 the Grothendieck Hilbert scheme, which states that the lexicographic poi
Externí odkaz:
http://arxiv.org/abs/2002.10424
Autor:
Cid-Ruiz, Yairon, Ramkumar, Ritvik
Publikováno v:
In Journal of Algebra 15 December 2023 636:248-278