Related papers: A Counterexample for Subadditivity of Multiplier I…
Demailly, Ein and Lazarsfeld \cite{DEL} proved the subadditivity theorem for multiplier ideals, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals, on non-singular…
We exhibit a new subadditivity formula for test ideals on singular varieties using an argument similar to those of Demailly-Ein-Lazarsfeld and Hara-Yoshida. Any subadditivity formula for singular varieties must have a correction term that…
We present a counterexample to the conjecture of Bihan, Franz, McCrory, and van Hamel concerning the maximality of toric varieties. There exists a six dimensional projective toric variety X with the sum of the mod 2 Betti numbers of X(R)…
In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes,…
We present examples which show that in dimension higher than one or codimension higher than two, there exist toric ideals I_A such that no binomial ideal contained in I_A and of the same dimension is a complete intersection. This result has…
Hara, Takemura and Yoshida discuss toric ideals arising from two way subtable sum problems and shows that these toric ideals are generated by quadratic binomials if and only if the subtables are either diagonal or triangular. In the present…
We present a construction of noncommutative double mirrors to complete intersections in toric varieties. This construction unifies existing sporadic examples and explains the underlying combinatorial and physical reasons for their…
As a generalization of formulas given by Demailly-Ein-Lazarsfeld, Eisenstein and Takagi, we prove a subadditivity formula for multiplier ideals associated to log pairs.
Given a set $\mathcal A = \{a_1,\ldots,a_n\} \subset \mathbb{N}^m$ of nonzero vectors defining a simplicial toric ideal $I_{\mathcal A} \subset k[x_1,...,x_n]$, where $k$ is an arbitrary field, we provide an algorithm for checking whether…
We define a version of multiplier ideals, the Mather multiplier ideals, on a variety with arbitrary singularities, using the Mather discrepancy and the Jacobian ideal. In this context we prove a relative vanishing theorem, thus obtaining…
An equivariant linear system on a toric variety is a linear system invariant under the torus action. We study the number of irreducible components of the complete intersection of general divisors from a fixed collection of equivariant…
We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.
In this article we give explicit descriptions of the multiplicities of some classes of monomial ideals. For instance, we give a formula for the multiplicities of all codimension 1 monomial ideals, and another formula for the multiplicities…
Let $X\subset \mathbb P^d$ be a $m$-dimensional variety in $d$-dimensional projective space. Let $k$ be a positive integer such that $\binom{m+k}k \le d$. Consider the following interpolation problem: does there exist a variety $Y\subset…
Given an effective Q-divisor D on a smooth complex variety, one can associate to D its multiplier ideal sheaf J(D), which measures in a somewhat subtle way the singularities of D. Because of their strong vanishing properties, these ideals…
The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads…
A simple formula computing the multiplier ideal of a monomial ideal on an arbitrary affine toric variety is given. Variants for the multiplier module and test ideals are also treated.
Let $n$ be an even natural number. We compute the periods of any $\frac{n}{2}$-dimensional complete intersection algebraic cycle inside an $n$-dimensional non-degenerated intersection of a projective simplicial toric variety. Using this…
This paper provides a formula for the Mather-Jacobian multiplier ideals of torus invariant ideals on (not necessarily normal) toric varieties that generalizes Howald's formula for the multiplier ideal of monomial ideals in a polynomial…
Let X be a complete toric variety with homogeneous coordinate ring S. In this article, we compute upper and lower bounds for the codimension in the critical degree of ideals of S generated by dim(X)+1 homogeneous polynomials that don't…