@misc{MartinSuess, author = {Martin, Bernd and S{\"u}ß, Hendrik}, title = {Milnor algebras could be isomorphic to modular algebras}, language = {en} } @incollection{Siebert, author = {Siebert, Thomas}, title = {Algorithms for the computation of free resolutions}, language = {en} } @misc{SuessHausen, author = {S{\"u}ß, Hendrik and Hausen, J{\"u}rgen}, title = {The Cox ring of an algebraic variety with torus action}, series = {Advances in Mathematics}, volume = {225}, journal = {Advances in Mathematics}, number = {2}, issn = {0001-8708}, doi = {doi:10.1016/j.aim.2010.03.010}, pages = {977 -- 1012}, language = {en} } @misc{SuessHausenHerppich, author = {S{\"u}ß, Hendrik and Hausen, J{\"u}rgen and Herppich, Elaine}, title = {Multigraded Factorial Rings and Fano varieties with torus action}, series = {Documenta Mathematica}, volume = {16}, journal = {Documenta Mathematica}, issn = {1431-0635}, pages = {71 -- 109}, abstract = {In a first result, we describe all finitely generated factorial algebras over an algebraically closed field of characteristic zero that come with an effective multigrading of complexity one by means of generators and relations. This enables us to construct systematically varieties with free divisor class group and a complexity one torus action via their Cox rings. For the Fano varieties of this type that have a free divisor class group of rank one, we provide explicit bounds for the number of possible deformation types depending on the dimension and the index of the Picard group in the divisor class group. As a consequence, one can produce classification lists for fixed dimension and Picard index. We carry this out expemplarily in the following cases. There are 15 non-toric surfaces with Picard index at most six. Moreover, there are 116 non-toric threefolds with Picard index at most two; nine of them are locally factorial, i.e. of Picard index one, and among these one is smooth, six have canonical singularities and two have non-canonical singularities. Finally, there are 67 non-toric locally factorial fourfolds and two one-dimensional families of non-toric locally factorial fourfolds. In all cases, we list the Cox rings explicitly.}, language = {en} } @misc{SuessIlten, author = {S{\"u}ß, Hendrik and Ilten, Nathan Owen}, title = {Polarized complexity-1 T-varieties}, series = {Michigan Mathematical Journal}, volume = {60}, journal = {Michigan Mathematical Journal}, number = {3}, pages = {561 -- 578}, abstract = {We describe polarized complexity-one T-varieties combinatorially in terms of so-called divisorial polytopes, and show how geometric properties of such a variety can be read off the corresponding divisorial polytope. We compare our description with other possible descriptions of polarized complexity-one T-varieties. We also describe how to explicitly find generators of affine complexity-one T-varieties.}, language = {en} } @misc{MartinLavandoskyy, author = {Martin, Bernd and Lavandoskyy, Victor}, title = {A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations}, series = {arXiv.org : (math-ph)}, journal = {arXiv.org : (math-ph)}, pages = {24}, language = {en} } @misc{MartinHirsch, author = {Martin, Bernd and Hirsch, Tobias}, title = {Deformation with sections: Cotangent cohomology, flatnes conditions and modular germs}, series = {arXiv.org : (math.CV)}, journal = {arXiv.org : (math.CV)}, pages = {26}, language = {en} } @incollection{Hirsch, author = {Hirsch, Tobias}, title = {Computing the Integral Closure of an Ideal Using its Rees Algebra}, series = {Computational commutative and non-commutative algebraic geometry, proceedings of the Nato Advanced Research Workshop on Computational Commutative and Non-Commutative Algebraic Geometry, Chisinau, Moldova, 6 - 11 June 2004}, booktitle = {Computational commutative and non-commutative algebraic geometry, proceedings of the Nato Advanced Research Workshop on Computational Commutative and Non-Commutative Algebraic Geometry, Chisinau, Moldova, 6 - 11 June 2004}, publisher = {IOS Press}, address = {Amsterdam [u.a.]}, isbn = {1-586-03505-3}, pages = {145 -- 155}, language = {en} } @incollection{MartinHirsch, author = {Martin, Bernd and Hirsch, Tobias}, title = {Modular Strata of Deformation Functors}, series = {Computational commutative and non-commutative algebraic geometry, proceedings of the Nato Advanced Research Workshop on Computational Commutative and Non-Commutative Algebraic Geometry, Chisinau, Moldova, 6 - 11 June 2004}, booktitle = {Computational commutative and non-commutative algebraic geometry, proceedings of the Nato Advanced Research Workshop on Computational Commutative and Non-Commutative Algebraic Geometry, Chisinau, Moldova, 6 - 11 June 2004}, publisher = {IOS Press}, address = {Amsterdam [u.a.]}, isbn = {1-586-03505-3}, pages = {156 -- 166}, language = {en} } @misc{PetersenSuess, author = {Petersen, Lars and S{\"u}ß, Hendrik}, title = {Torus invariant divisors}, series = {Israel Journal of Mathematics}, volume = {182}, journal = {Israel Journal of Mathematics}, number = {1}, issn = {0021-2172}, pages = {481 -- 504}, abstract = {Using the language of Altmann, Hausen and S{\"u}ß, we describe invariant divisors on normal varieties X which admit an effective codimension one torus action. In this picture, X is given by a divisorial fan on a smooth projective curve Y. Cartierdivisors on X can be described by piecewise affine functions h on the divisorial fan S whereas Weil divisors correspond to certain zero and one-dimensional faces of it. Furthermore, we provide descriptions of the divisor class group and the canonical divisor. Global sections of line bundles O(D h ) will be determined by a subset of a weight polytope associatedto h, and global sections of specific line bundles on the underlying curve Y.}, language = {en} } @misc{MartinPochekutov, author = {Martin, Bernd and Pochekutov, Dimitry}, title = {Discriminant and Singularities of Logarithmic Gauss Map, Examples and Application}, series = {Journal of Siberian Federal University, Mathematik \& Physics}, volume = {6}, journal = {Journal of Siberian Federal University, Mathematik \& Physics}, number = {1}, issn = {1997-1397}, pages = {74 -- 85}, abstract = {The study of hypersurfaces in a torus leads to the beautiful zoo of amoebas and their contours, whose possible configurations are seen from combinatorial data. There is a deep connection to the logarithmic Gauss map and its critical points. The theory has a lot of applications in many directions. In this report we recall basic notions and results from the theory of amoebas, show some connection to algebraic singularity theory and discuss some consequences from the well known classification of singularities to this subject. Moreover, we have tried to compute some examples using the computer algebra system SINGULAR and discuss different possibilities and their effectivity to compute the critical points. Here we meet an essential obstacle: Relevant examples need real or even rational solutions, which are found only by chance. We have tried to unify different views to that subject.}, language = {en} } @incollection{Martin, author = {Martin, Bernd}, title = {Computing versal deformations with SINGULAR}, language = {en} } @incollection{Martin, author = {Martin, Bernd}, title = {Modular lines for singularities of the T-seris}, language = {en} } @article{SuessAltmannHausen, author = {S{\"u}ß, Hendrik and Altmann, Klaus and Hausen, J{\"u}rgen}, title = {Gluing affine torus actions via divisorial fans}, language = {en} } @article{SuessIlten, author = {S{\"u}ß, Hendrik and Ilten, Nathan Owen}, title = {AG Codes from Polyhedral Divisors}, series = {arXiv.org : [math.AG]}, journal = {arXiv.org : [math.AG]}, pages = {30}, language = {en} } @article{MartinGrassmannGreueletal., author = {Martin, Bernd and Grassmann, H. and Greuel, G.-M. and Neumann, W. and Pfister, Gerhard and Pohl, W. and Sch{\"o}nemann, H. and Siebert, Thomas}, title = {On an implementation of standard bases and syzygies in SINGULAR}, language = {en} } @article{MartinHirsch, author = {Martin, Bernd and Hirsch, Tobias}, title = {Deformations with section: Cotangent cohomology, flatness and modular subspaces}, language = {en} } @article{MartinAleksandrov, author = {Martin, Bernd and Aleksandrov, Aleksandr}, title = {Gauss-Manin connection associated with bouquets of curves}, language = {en} } @article{Siebert, author = {Siebert, Thomas}, title = {Recursive computation of free resolutions and a generalized Koszul complex}, language = {en} } @article{MartinSuess, author = {Martin, Bernd and S{\"u}ß, Hendrik}, title = {Milnor algebras versus modular germs for unimodal hypersurface singularities}, language = {en} } @article{MartinPfisterPopescu, author = {Martin, Bernd and Pfister, Gerhard and Popescu, Dorin}, title = {Maximal Cohen-Macaulay modules over rings of type xt+y3}, language = {en} } @article{MartinSiebert, author = {Martin, Bernd and Siebert, Thomas}, title = {Graded Lie algebras and quasihomogeneous complete intersection singularities}, language = {en} } @article{MartinAleksandrov, author = {Martin, Bernd and Aleksandrov, Aleksandr}, title = {Derivations and deformations of artinian algebras}, language = {en} } @article{Martin, author = {Martin, Bernd}, title = {Coarse moduli space of ordinary multiple points in the plane}, language = {en} } @article{Martin, author = {Martin, Bernd}, title = {Modular deformations and space curve singularities}, language = {en} } @article{MartinAleksandrov, author = {Martin, Bernd and Aleksandrov, Aleksandr}, title = {Gauss-Manin connection for bouquets of curves}, language = {en} } @article{Martin, author = {Martin, Bernd}, title = {Svijasanost Gaussa-Manina dlja buketov krivich}, language = {ru} } @article{Martin, author = {Martin, Bernd}, title = {Algorithmic Computation of Flattenings and of Modular Deformations}, publisher = {Elsevier}, language = {en} } @phdthesis{Hirsch, author = {Hirsch, Tobias}, title = {Modular deformations of isolated singularities}, publisher = {Brandenburgische Techn. Univ.}, address = {Cottbus}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-000000538}, language = {en} } @techreport{MartinPalamodov, author = {Martin, Bernd and Palamodov, Victor P.}, title = {Discrete and modular deformations of singularities, applications}, publisher = {BTU, Institut f{\"u}r Mathematik}, address = {Cottbus}, pages = {30}, language = {en} } @techreport{MartinSiebert, author = {Martin, Bernd and Siebert, Thomas}, title = {Splitting algorithm for vector bundles}, publisher = {Univ.}, address = {Kaiserslautern}, pages = {16}, language = {en} } @techreport{Hirsch, author = {Hirsch, Tobias}, title = {Computing the integral closure of an ideal using its Rees algebra}, publisher = {BTU, Institut f{\"u}r Mathematik}, address = {Cottbus}, pages = {9}, language = {en} }