| 1. |
|
|
| 2. |
- Brown, Gavin, et al.
(författare)
-
Tutorial on Tom and Jerry: The two smoothings of the anticanonical cone over P(1; 2; 3)
- 2021
-
Ingår i: EMS Surveys in Mathematical Sciences. - 2308-216X .- 2308-2151. ; 8:1, s. 25-38
-
Tidskriftsartikel (refereegranskat)abstract
- This is a first introduction to unprojection methods, and more specifically to Tom and Jerry unprojections. These two harmless tricks deserve to be better known, since they answer many practical questions about constructing codimension 4 Gorenstein subschemes. In particular, we discuss here the two smoothing components of the anticanonical cone over P.1; 2; 3/.
|
|
| 3. |
- Brown, G., et al.
(författare)
-
Tutorial on Tom and Jerry: the two smoothings of the anticanonical cone over P(1, 2, 3)
- 2021
-
Ingår i: Ems Surveys in Mathematical Sciences. - : European Mathematical Society - EMS - Publishing House GmbH. - 2308-2151. ; 8:1-2, s. 25-38
-
Tidskriftsartikel (refereegranskat)abstract
- This is a first introduction to unprojection methods, and more specifically to Tom and Jerry unprojections. These two harmless tricks deserve to be better known, since they answer many practical questions about constructing codimension 4 Gorenstein subschemes. In particular, we discuss here the two smoothing components of the anticanonical cone over P(1, 2, 3).
|
|
| 4. |
|
|
| 5. |
- Fisher, J. Chris, et al.
(författare)
-
Circle incidence theorems
- 2015
-
Ingår i: Forum Geometricorum: A Journal on Classical Euclidean Geometry. - 1534-1178. ; 15, s. 211-228
-
Tidskriftsartikel (refereegranskat)abstract
- Larry Hoehn discovered a remarkable concurrence theorem about pentagrams. Draw circles through two consecutive vertices and the intersection points of the sides in between. Then the radical axes of each pair of consecutive circles are concurrent or parallel. In this note we prove a generalization to n-gons.
|
|
| 6. |
- Heinrich, Katharina, et al.
(författare)
-
The space of twisted cubics
- 2021
-
Ingår i: Epijournal de Geometrie Algebrique. - : Centre pour la Communication Scientifique Directe (CCSD). - 2491-6765. ; 5, s. 1-22
-
Tidskriftsartikel (refereegranskat)abstract
- We consider the Cohen-Macaulay compactification of the space of twisted cubics in Pn. This compactification is the fine moduli scheme representing the functor of CM-curves with Hilbert polynomial 3t + 1. We show that the moduli scheme of CM-curves in P3 is isomorphic to the twisted cubic component of the Hilbert scheme. We also describe the compactification for twisted cubics in Pn
|
|
| 7. |
- Stevens, Jan, 1955
(författare)
-
Computing Versal Deformations of Singularities with Hauser's Algorithm.
- 2013
-
Ingår i: Deformations of Surface Singularities. Series: Bolyai Society Mathematical Studies, Vol. 23. Némethi, Andras; Szilárd, Agnes (Eds.). - Berlin : Springer. - 9783642391309 ; , s. 203-228
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Hauser’s algorithm provides an alternative approach to the computation of versal deformations, not based on step by step extending infinitesimal deformations. We use this method to compute nontrivial examples.
|
|
| 8. |
- Stevens, Jan, 1955
(författare)
-
Conjectures on Stably Newton Degenerate Singularities
- 2021
-
Ingår i: Arnold Mathematical Journal. - : Springer Science and Business Media LLC. - 2199-6792 .- 2199-6806. ; 7:3, s. 441-465
-
Tidskriftsartikel (refereegranskat)abstract
- We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions. We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, xp+ xq in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.
|
|
| 9. |
- Stevens, Jan, 1955
(författare)
-
Deforming nonnormal isolated surface singularities and constructing 3-folds with P^1 as exceptional set
- 2015
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as isolated, non Cohen-Macaulay threefold singularities. They arise by a small contraction of a smooth rational curve, whose normal bundle has a sufficiently positive subbundle. We study such singularities from their nonnormal general hyperplane section.
|
|
| 10. |
- Stevens, Jan, 1955
(författare)
-
Deforming nonnormal isolated surface singularities and constructing threefolds with P1 as exceptional set
- 2017
-
Ingår i: Singularities and Computer Algebra: Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday. - Cham : Springer International Publishing. - 9783319288284 ; , s. 329-351
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as isolated, non-Cohen-Macaulay threefold singularities. They arise by a small contraction of a smooth rational curve, whose normal bundle has a sufficiently positive subbundle. We study such singularities from their nonnormal general hyperplane section.
|
|
