#### 240 Citations

TOWARDS CLASSIFYING TORIC DEGENERATIONS OF CUBIC SURFACES MARIA DONTEN-BURY-PAUL GÖRLACH-MILENA WROBEL

- 2019

We investigate the class of degenerations of smooth cubic surfaces which are obtained from degenerating their Cox rings to toric algebras. More precisely, we work in the spirit of Sturmfels and Xu… Expand

Symbolic Rees algebras.

- Mathematics
- 2020

We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a… Expand

The resurgence of an ideal with Noetherian symbolic Rees algebra is rational

- Mathematics
- 2020

We show that if an ideal in a polynomial ring has a Noetherian symbolic Rees algebra then two statistics which measure the relationship between its regular and symbolic powers are both rational;… Expand

Constructing quotients of algebraic varieties by linear algebraic group actions

- Mathematics
- 2015

In this article we review the question of constructing geometric quotients of actions of linear algebraic groups on irreducible varieties over algebraically closed fields of characteristic zero, in… Expand

Linear subspaces, symbolic powers and Nagata type conjectures

- Mathematics
- 2014

Abstract Inspired by results of Guardo, Van Tuyl and the second author for lines in P 3 , we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m… Expand

LIMITS IN COMMUTATIVE ALGEBRA AND ALGEBRAIC GEOMETRY

- 2013

This article is on the general theme of limits arising in commutative algebra and algebraic geometry, in asymptotic multiplicity and regularity. The four sections of this article are based on the… Expand

Nagata type statements

- Mathematics
- 2017

Nagata solved Hilbert's 14-th problem in 1958 in the negative. The solution naturally lead him to a tantalizing conjecture that remains widely open after more than half a century of intense efforts.… Expand

Single point Seshadri constants on rational surfaces

- Mathematics
- 2017

Motivated by a similar result of Dumnicki, K\"uronya, Maclean and Szemberg under a slightly stronger hypothesis, we exhibit irrational single-point Seshadri constants on a rational surface $X$… Expand

Invariant theory of relatively free right-symmetric and Novikov algebras

- Mathematics
- 2016

Algebras with the polynomial identity (x,y,z)=(x,z,y), where (x,y,z)=x(yz)-(xy)z is the associator, are called right-symmetric. Novikov algebras are right-symmetric algebras satisfying additionally… Expand

Limits in commutative algebraand algebraic geometry

- 2015

This article is on the general theme of limits arising in commutative algebra and algebraic geometry, in asymptotic multiplicity and rgularity. The four sections of this article are based on the four… Expand