Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

In this paper, when (1<p<2), we establish the (C^{1,alpha }_{,textrm{loc},})-regularity of weak solutions to the degenerate subelliptic p-Laplacian equation

on SU(3) endowed with the horizontal vector fields (X_1,dots ,X_6). The result can be extended to a class of compact connected semi-simple Lie group.

In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form ({mathbb {L}}^4(delta )) with constant sectional curvature (delta ). We obtain some local classifications of biconservative CMC surfaces in ({mathbb {L}}^4(delta )). Further, we get complete classification of biharmonic CMC surfaces in the de Sitter 4-space. We also proved that there is no biharmonic CMC surface in the anti-de Sitter 4-space. Further, we get the classification of biconservative, quasi-minimal surfaces in Minkowski-4 space.

We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For (nin {2,3,4}), we show that, generically in all but a finite number of irreducible components of the moduli space of polarized (textrm{Kum}^n)-type varieties, the polarization is base-point-free. We also prove generic base-point-freeness in the moduli space in all dimensions if the polarization has divisibility one.

In his 2008 thesis [16] , Tateno claimed a counterexample to the Bonato–Tardif conjecture regarding the number of equimorphy classes of trees. In this paper we revisit Tateno’s unpublished ideas to provide a rigorous exposition, constructing locally finite trees having an arbitrary finite number of equimorphy classes; an adaptation provides partial orders with a similar conclusion. At the same time these examples also disprove conjectures by Thomassé and Tyomkyn.

We study lines on smooth cubic surfaces over the field of p-adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines are 0, 1, 2, 3, 5, 7, 9, 15 or 27. We show that each of these counts is achieved. Probabilistic aspects are investigated by sampling both p-adic and real cubic surfaces from different distributions and estimating the probability of each count.We link this to recent results on probabilistic enumerative geometry. Some experimental results on the Galois groups attached to p-adic cubic surfaces are also discussed.

We call a smooth irreducible projective curve a Castelnuovo curve if it admits a birational map into the projective r-space such that the image curve has degree at least 2r+1 and the maximum possible geometric genus (which one can calculate by a classical formula due to Castelnuovo). It is well known that a Castelnuovo curve must lie on a Hirzebruch surface (rational ruled surface). Conversely, making use of a result of W. Castryck and F. Cools concerning the scrollar invariants of curves on Hirzebruch surfaces we show that curves on Hirzebruch surfaces are Castelnuovo curves unless their genus becomes too small w.r.t. their gonality. We analyze the situation more closely, and we calculate the number of moduli of curves of fixed genus g and fixed gonality k lying on Hirzebruch surfaces, in terms of g and k.

In 2020 S. M. Gonek, S. W. Graham and Y. Lee formulated the Lindelöf hypothesis for prime numbers and proved that it is equivalent to the Riemann Hypothesis. In this note we show that their result holds in the Selberg class of L-functions.

We find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra (I{mathfrak u}_n{:}{=}{mathfrak u}_n < imes {mathfrak u}_n^*), where ({mathfrak u}_n) is the Lie algebra of upper triangular (ntimes n) matrices. Our results also extend to (mathfrak {gl}_{n+}^epsilon ), a “solvable approximation” of (mathfrak {gl}_n), as defined within.

We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a semi-universal deformation. These results generalize the analogous results in complex analytic geometry first independently proved by A. Douady and H. Grauert in the ’70. We follow Douady’s two steps process approach consisting of an infinite-dimensional construction of the deformation space followed by a finite-dimensional reduction.