6 papers
The rank of the permanent tensor is sixteen
Jong In Han, Jeyoung Song
In this paper, we show that the tensor rank of the permanent tensor is at least over and its subfields, which matches the known upper bound. The $5\ti…
The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities
Jong In Han
For a nondegenerate projective variety , the Eisenbud-Goto conjecture asserts that . Despite the existence of…
Hierarchical structure of graded Betti numbers in the quadratic strand
Jong In Han, Sijong Kwak, Wanseok Lee
The classical results, initiated by Castelnuovo and Fano and later refined by Eisenbud and Harris, provide several upper bounds on the number of quadrics defining a nondegenerate p…
Characterization of projective varieties beyond varieties of minimal degree and del Pezzo varieties
Jong In Han, Sijong Kwak, Euisung Park
Varieties of minimal degree and del Pezzo varieties are basic objects in projective algebraic geometry. Those varieties have been characterized and classified for a long time in ma…
Surface counterexamples to the Eisenbud-Goto conjecture
Jong In Han, Sijong Kwak
It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb…
On quadratic persistence and Pythagoras numbers of totally real projective varieties
Jong In Han, Jaewoo Jung, Euisung Park
In this paper, we study the relationship between quadratic persistence and the Pythagoras number of totally real projective varieties. Building upon the foundational work of Blekhe…