Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Thomas Markwig"'
Autor:
Yue Ren, Thomas Markwig
Publikováno v:
Journal of Symbolic Computation. 83:315-341
We generalise the notion of a Grobner fan to ideals in R 〚 t 〛 [ x 1 , … , x n ] for certain classes of coefficient rings R and give a constructive proof that the Grobner fan is a rational polyhedral fan. For this we introduce the notion of ini
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94c6870d793b230ae6afda419d0254b0
https://doi.org/10.1016/j.jsc.2016.11.016
https://doi.org/10.1016/j.jsc.2016.11.016
The family of complex projective surfaces in P 3 \mathbb {P}^3 of degree d d having precisely δ \delta nodes as their only singularities has codimension δ \delta in the linear system | O P 3 ( d ) | |{\mathcal O}_{\mathbb {P}^3}(d)| for sufficientl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::69279937fd90f5d980cc246072236ab1
Publikováno v:
Manuscripta Mathematica. 137:383-418
In this paper, we study tropicalisations of families of curves with a singularity in a fixed point. The tropicalisation of such a family is a linear tropical variety. We describe its maximal dimensional cones using results about linear tropical varie
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b868d4dcd640778be7bbd3d11f7f4a88
https://doi.org/10.1007/s00229-011-0471-8
https://doi.org/10.1007/s00229-011-0471-8
Publikováno v:
Revista Matemática Complutense. 25:61-85
We study singularities f in K[[x_1,...,x_n]] over an algebraically closed field K of arbitrary characteristic with respect to right respectively contact equivalence, and we establish that the finiteness of the Milnor respectively the Tjurina number i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d9cfabfae04f129da69134c297f8c94
https://doi.org/10.1007/s13163-010-0056-1
https://doi.org/10.1007/s13163-010-0056-1
Publikováno v:
LMS Journal of Computation and Mathematics. 12:275-294
If (Q,A) is a marked polygon with one interior point, then a general polynomialfbelonging toK[x,y] with supportAdefines an elliptic curveCfon the toric surfaceXA. IfKhas a non-archimedean valuation intoRwe can tropicalizeCfto get a tropical curve Tro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16a8de58583234fc01ee19be90d7f763
https://doi.org/10.1112/s1461157000001522
https://doi.org/10.1112/s1461157000001522
Autor:
Thomas Markwig
Publikováno v:
Journal of Symbolic Computation. 43:765-786
In this paper we study standard bases for submodules of K[[t"1,...,t"m]][x"1,...,x"n]^s respectively of their localisation with respect to a t@?-local monomial ordering. The main step is to prove the existence of a division with remainder generalisin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c29b5b14d4195ba70cc5338e4b085ec3
https://doi.org/10.1016/j.jsc.2008.03.003
https://doi.org/10.1016/j.jsc.2008.03.003
Publikováno v:
Journal of Algebra. 320(10):3832-3848
Several results in tropical geometry have related the j-invariant of an algebraic plane curve of genus one to the cycle length of a tropical curve of genus one. In this paper, we prove that for a plane cubic over the field of Puiseux series the negat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7e03b2ebb3b97a3502edc9ef8a245811
Autor:
Thomas Markwig, Luca Chiantini
Publikováno v:
Journal of Pure and Applied Algebra. 212(6):1337-1346
In arXive:0705.3912 we studied triple-point defective very ample linear systems on regular surfaces, and we showed that they can only exist if the surface is ruled. In the present paper we show that we can drop the regularity assumption, and we class
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::309c4f43c41656273c3e5cf8630d6ad8
Autor:
Thomas Markwig, Yue Ren
We show how tropical varieties of ideals I over a field K with non-trivial valuation can be traced back to tropical varieties of ideals in R[[t]][x] over some dense subring R in its ring of integers. Moreover, for homogeneous ideals, we present algor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d9b6ef407797a80511edc1221a5ef13
We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we develop a three
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0f9b36a7fb2afde52f4d36d4433f1b7
http://arxiv.org/abs/1503.08593
http://arxiv.org/abs/1503.08593