The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Eugenii Shustin - One of the best experts on this subject based on the ideXlab platform.
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Singular Welschinger invariants
arXiv: Algebraic Geometry, 2019Co-Authors: Eugenii ShustinAbstract:We suggest an invariant way to enumerate nodal and nodal-cuspidal Real deformations of Real Plane curve singularities. The key idea is to assign Welschinger signs to the counted deformations. Our invariants can be viewed as a local version of Welschinger invariants enumerating Real Plane rational curves.
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morsifications of Real Plane curve singularities
arXiv: Algebraic Geometry, 2017Co-Authors: Peter Leviant, Eugenii ShustinAbstract:A Real morsification of a Real Plane curve singularity is a Real deformation given by a family of Real analytic functions having only Real Morse critical points with all saddles on the zero level. We prove the existence of Real morsifications for Real Plane curve singularities having arbitrary Real local branches and pairs of complex conjugate branches satisfying some conditions. This was known before only in the case of all local branches being Real (A'Campo, Gusein-Zade). We also discuss a relation between Real morsifications and the topology of singularities, extending to arbitrary Real morsifications the Balke-Kaenders theorem, which states that the A'Campo--Gusein-Zade diagram associated to a morsification uniquely determines the topological type of a singularity.
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Welschinger invariant and enumeration of Real Plane rational curves
arXiv: Algebraic Geometry, 2003Co-Authors: Ilia Itenberg, Viatcheslav Kharlamov, Eugenii ShustinAbstract:Welschinger's invariant bounds from below the number of Real rational curves through a given generic collection of Real points in the Real projective Plane. We estimate this invariant using Mikhalkin's approach which deals with a corresponding count of tropical curves. In particular, our estimate implies that, for any positive integer $d$, there exists a Real rational curve of degree $d$ through any collection of $3d-1$ Real points in the projective Plane, and, moreover, asymptotically in the logarithmic scale at least one third of the complex Plane rational curves through a generic point collection are Real. We also obtain similar results for curves on other toric Del Pezzo surfaces.
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Maximal smoothings of Real Plane curve singular points.
1998Co-Authors: Viatcheslav Kharlamov, Jean-jacques Risler, Eugenii ShustinAbstract:The local Harnack inequality bounds from above the number of ovals which can appear in a small perturbation of a singular point. As is known, there are singular points for which this bound is not sharp. We show that Harnack inequality is sharp in any complex topologically equisingular class: every Real Plane curve singular point is complex deformation equivalent to a Real singularity for which Harnack inequality is sharp. For semi-quasi-homogeneous and some other singularities we exhibit a Real deformation with the same property. A refined Harnack inequality and its sharpness are discussed also.
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Real Plane algebraic curves with prescribed singularities
Topology, 1993Co-Authors: Eugenii ShustinAbstract:IN THIS article we deal with the classical problem about a number of prescribed singularities on a Plane algebraic curve of a given degree. We present constructions of Real Plane algebraic curves of a given degree with arbitrary singularities. In particular, we get irreducible curves of degree d with any number of Real cusps between 0 and d2/4 + O(d). It is well-known [9] that for any positive integers d, m satisfying
Johannes Huisman - One of the best experts on this subject based on the ideXlab platform.
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a geometric description of the neutral component of the jacobian of a Real Plane curve having many pseudo lines
Mathematische Nachrichten, 2003Co-Authors: Goulwen Fichou, Johannes HuismanAbstract:A pseudo–line of a Real Plane curve is a Real branch that is not homologically trivial in ℙ2(ℝ). A Real Plane curve C of degree d is said to have many pseudo–lines if it has exactly d – 2 pseudo–lines and if the genus of its normalization C is equal to d – 2. Let C be such a curve. We give a planar description of the neutral component of the set of Real points of the Jacobian of the normalization C of C.
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A geometric description of the neutral component of the Jacobian of a Real Plane curve having many pseudo–lines
Mathematische Nachrichten, 2003Co-Authors: Goulwen Fichou, Johannes HuismanAbstract:A pseudo–line of a Real Plane curve is a Real branch that is not homologically trivial in ℙ2(ℝ). A Real Plane curve C of degree d is said to have many pseudo–lines if it has exactly d – 2 pseudo–lines and if the genus of its normalization C is equal to d – 2. Let C be such a curve. We give a planar description of the neutral component of the set of Real points of the Jacobian of the normalization C of C.
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On the enumerative geometry of Real algebraic curves having many Real branches
Advances in Geometry, 2003Co-Authors: Johannes HuismanAbstract:Let C be a smooth Real Plane curve. Let c be its degree and g its genus. We assume that C has at least g Real branches. Let d be a nonzero natural integer strictly less than c. Let e be a partition of cd of length g. Let n be the number of all Real Plane curves of degree d that are tangent to g Real branches of C with orders of tangency e1; .. .; eg. We show that n is finite and we determine n explicitly.
Jacek Marchwicki - One of the best experts on this subject based on the ideXlab platform.
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Levy–Steinitz theorem and achievement sets of conditionally convergent series on the Real Plane
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Szymon Gła̧b, Jacek MarchwickiAbstract:Abstract Levy–Steinitz theorem characterizes the sum range of conditionally convergent series, that is a set of all its convergent rearrangements; in finitely dimensional spaces – it is an affine subspace. An achievement of a series is a set of all its subsums. We study the properties of achievement sets of series whose sum range is the whole Plane. It turns out that it varies on the number of Levy vectors of a series.
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levy steinitz theorem and achievement sets of conditionally convergent series on the Real Plane
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Szymon Glab, Jacek MarchwickiAbstract:Abstract Levy–Steinitz theorem characterizes the sum range of conditionally convergent series, that is a set of all its convergent rearrangements; in finitely dimensional spaces – it is an affine subspace. An achievement of a series is a set of all its subsums. We study the properties of achievement sets of series whose sum range is the whole Plane. It turns out that it varies on the number of Levy vectors of a series.
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levy steinitz theorem and achievement sets of conditionally convergent series on the Real Plane
arXiv: Functional Analysis, 2017Co-Authors: Szymon Glab, Jacek MarchwickiAbstract:Levy-Steinitz theorem characterize sum range of conditionally convergent series, that is a set of all its convergent rearrangements; in finitely dimensional spaces -- it is an affine subspace. An achievement of a series is a set of all its subsums. We study the properties of achievement sets of series whose sum range is the whole Plane. It turns out that it varies on the number of Levy vectors of a series.
Adam Trybus - One of the best experts on this subject based on the ideXlab platform.
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Rational Region-Based Affine Logic of the Real Plane
ACM Transactions on Computational Logic, 2016Co-Authors: Adam TrybusAbstract:The region-based spatial logics, where variables are set to range over certain subsets of geometric space, are the focal point of the qualitative spatial reasoning, a subfield of the KRR 〈ROQ(R2), convM, ≤M〉, where ROQ(R2) is the set of regular open rational polygons of the Real Plane; convM is the convexity property and ≤M is the inclusion relation. The axiomatisation uses two infinitary rules of inference and a number of axiom schemas.
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an axiom system for a spatial logic with convexity
European Conference on Artificial Intelligence, 2010Co-Authors: Adam TrybusAbstract:This paper presents a part of work in progress on axiomatizing a spatial logic with convexity and inclusion predicates (hereinafter called convexity logic), with some intended interpretation over the Real Plane. More formally, let Lconv,≤ be a language of first order logic and two non-logical primitives: conv (interpreted as a property of a set of being convex) and ≤ (interpreted as the set inclusion relation). We let variables range over regular open rational polygons in the Real Plane (denoted ROQ(R2)). We call the tuple M = ---where primitives are defined as indicated above ---a standard model. We propose an axiomatization of the theory of M and prove soundness and completeness for this axiomatization.
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ECAI - An Axiom System for a Spatial Logic with Convexity
2010Co-Authors: Adam TrybusAbstract:This paper presents a part of work in progress on axiomatizing a spatial logic with convexity and inclusion predicates (hereinafter called convexity logic), with some intended interpretation over the Real Plane. More formally, let Lconv,≤ be a language of first order logic and two non-logical primitives: conv (interpreted as a property of a set of being convex) and ≤ (interpreted as the set inclusion relation). We let variables range over regular open rational polygons in the Real Plane (denoted ROQ(R2)). We call the tuple M = ---where primitives are defined as indicated above ---a standard model. We propose an axiomatization of the theory of M and prove soundness and completeness for this axiomatization.
Egor Yasinsky - One of the best experts on this subject based on the ideXlab platform.
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Automorphisms of Real del Pezzo surfaces and the Real Plane Cremona group
arXiv: Algebraic Geometry, 2019Co-Authors: Egor YasinskyAbstract:We study automorphism groups of Real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the Real Plane Cremona group.
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p -Subgroups in Automorphism Groups of Real del Pezzo Surfaces
Doklady Mathematics, 2018Co-Authors: Egor YasinskyAbstract:We classify finite p-groups acting minimally on Real del Pezzo surfaces. This gives a partial classification of p-subgroups in the Real Plane Cremona group.
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Subgroups of odd order in the Real Plane Cremona group
Journal of Algebra, 2016Co-Authors: Egor YasinskyAbstract:Abstract In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the Real projective Plane.
