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Stepan Yu. Orevkov

Publications and source records attributed to Stepan Yu. Orevkov.

8 recordsLinked to original sources
arXiv2026

Further Bounding the Kreuzer-Skarke Landscape

Batyrev's construction provides a map from fine, regular, star triangulations (FRSTs) of 4D reflexive polytopes to smooth Calabi-Yau threefolds (CYs). We prove that there are at most $10^{296}$ diffeomorphism classes of CYs produced in this manner, improving arXiv:2008.01730's upper bound of $10^{428}$. To show this, we make use of the fact that any two FRSTs with the same 2-face restrictions give rise to diffeomorphic CYs and bound the number of such '2-face equivalence classes' for all polytopes with Hodge number $h^{1,1} \geq 300$. We also put a lower bound of $10^{276}$ on the number of 2-face equivalence classes, but emphasize that this is not a lower bound on the number of diffeomorphism classes of CYs, as distinct 2-face equivalence classes may give rise to diffeomorphic threefolds.

hep-th↗
arXiv2017

Signatures of real algebraic curves via plumbing diagrams

We define and calculate signature and nullity invariants for complex schemes for curves in the real projective plane. We use an analog of the Murasugi-Tristram inequality to prohibit certain schemes from being realized by real algebraic curves. We give new formulas for Casson-Gordon invariants of graph manifolds, and signatures of graph links.

math.AG↗
arXiv2015

Algorithmic recognition of quasipositive 4-braids of algebraic length three

We give an algorithm to decide whether a given braid with four strings is a product of three factors which are conjugates of standard generators of the braid group. The algorithm is of polynomial time. It is based on the Garside theory. We give also a polynomial algorithm to decide if a given braid with any number of strings is a product of two factors which are conjugates of given powers of the standard generators (in my previous paper this problem was solved without polynomial estimates).

math.GR↗
arXiv2015

Criterion of Hurwitz equivalence for quasipositive factorizations of 3-braids

We consider the Hurwitz action on quasipositive factorizations of a 3-braid. In a previous paper, for any given 3-braid we described a certain finite set which contains at least one representative of each orbit. Here we give an algorithm to decide if two elements of this finite set belong to the same orbit.

math.GR↗
arXiv2014

On the Hurwitz action on quasipositive factorizations of 3-braids

We consider the Hurwitz action on quasipositive factorizations of 3-braids. We prove that every orbit contains an element of a special form. This fact provides an algorithm of finding representatives of every orbit for a given braid. We prove also that (1) any 3-braid has a finite number of orbits; (2) a Birman-Ko-Lee positive 3-braid has a single orbit; (3) a 3-braid of algebraic length two has at most two orbits.

math.GR↗
arXiv2014

Algorithmic recognition of quasipositive braids of algebraic length two

We give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group. The same problem is solved in a certain class of Garside groups including Artin-Tits groups of spherical type. The solution is based on the Garside theory and, especially, on the theory of cyclic sliding developed by Gebhardt and Gonzalez-Meneses. We show that if a braid is of the required form, then any cycling orbit in its sliding circuit set in the dual Garside structure contains an element for which this fact is immediately seen from the left normal form.

math.GR↗