Fixed point scheme of the Hilbert Scheme under a 1-dimensional additive algebraic group action

Download
2011
Özkan, Engin
In general we know that the fixed point locus of a 1-dimensional additive linear algebraic group,G_{a}, action over a complete nonsingular variety is connected. In thesis, we explicitly identify a subset of the G_{a}-fixed locus of the punctual Hilbert scheme of the d points,Hilb^{d}(P^{2}; 0),in P^{2}. In particular we give an other proof of the fact that Hilb^{d}(P^{2}; 0) is connected.

Suggestions

Finite type points on subsets of C-n
Yazıcı, Özcan (Elsevier BV, 2020-07-01)
In [4], D'Angelo introduced the notion of points of finite type for a real hypersurface M subset of C-n and showed that the set of points of finite type in M is open. Later, Lamel-Mir [8] considered a natural extension of D'Angelo's definition for an arbitrary set M subset of C-n. Building on D'Angelo's work, we prove the openness of the set of points of finite type for any subset M subset of C-n.
Knotting of algebraic curves in CP2
Finashin, Sergey (2002-01-01)
For any k⩾3, I construct infinitely many pairwise smoothly non-isotopic smooth surfaces homeomorphic to a non-singular algebraic curve of degree 2k, realizing the same homology class as such a curve and having abelian fundamental group ⧹ . This gives an answer to Problem 4.110 in the Kirby list (Kirby, Problems in low-dimensional topology, in: W. Kazez (Ed.), Geometric Topology, AMS/IP Stud. Adv. Math. vol 2.2, Amer. Math. Soc., Providence, 1997).
Almost periodic solutions of the linear differential equation with piecewise constant argument
Akhmet, Marat (2009-10-01)
The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Finite bisimulations for switched linear systems
Aydın Göl, Ebru; Lazar, Mircea; Belta, Calin (2013-02-04)
In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space and a switched linear system with stable subsystems, the proposed algorithm generates the bisimulation quotient in a finite number of steps with the aid of sublevel sets of a polyhedral Lyapunov function. Starting from a sublevel set that includes the origin in its interio...
Finite Bisimulations for Switched Linear Systems
Aydın Göl, Ebru; Lazar, Mircea; Belta, Calin (2014-12-01)
In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space and a switched linear system with stable subsystems, the proposed algorithm generates the bisimulation quotient in a finite number of steps with the aid of sublevel sets of a polyhedral Lyapunov function. Starting from a sublevel set that includes the origin in its interio...
Citation Formats
E. Özkan, “Fixed point scheme of the Hilbert Scheme under a 1-dimensional additive algebraic group action,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.