-
作者：Casalaina-Martin, Sebastian
摘要：For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym varieties. Applications of this theorem to cubic threefolds and Prym varieties of dimension five are also considered.
-
作者：Aleman, Alexandru; Richter, Stefan; Sundberg, Carl
摘要：Let mu be a finite positive measure on the closed disk (D) over bar in the complex plane, let 1 <= t < infinity, and let P-t(mu) denote the closure of the analytic polynomials in L-t(mu). We suppose that D is the set of analytic bounded point evaluations for P-t(mu), and that P-t(mu) contains no nontrivial characteristic functions. It is then known that the restriction of mu to partial derivative D must be of the form h vertical bar dz vertical bar. We prove that every function f is an element...
-
作者：Riviere, Tristan; Tian, Gang
摘要：We prove that 2 dimensional integer multiplicity 2 dimensional rectifiable currents which are almost complex cycles in an almost complex manifold admitting locally a compatible positive symplectic form are smooth surfaces aside from isolated points and therefore are J-holomorphic curves.
-
作者：Weber, Matthias; Hoffman, David; Wolf, Michael
摘要：There exists a properly embedded minimal surface of genus one with one end. The end is asymptotic to the end of the helicoid. This genus one helicoid is constructed as the limit of a continuous one-parameter family of screw-motion invariant minimal surfaces-also asymptotic to the helicoid-that have genus equal to one in the quotient.
-
作者：Tao, Terence; Vu, Van H.
摘要：Consider a random sum eta(1)nu(1) + ... + eta(n)nu(n), where eta(1), ... , eta(n) are independently and identically distributed (i.i.d.) random signs and nu(1), ... , nu(n) are integers. The Littlewood-Offord problem asks to maximize concentration probabilities such as P(eta(1)nu(1) + ... + eta(n)nu(n) = 0) subject to various hypotheses on nu(1), ... , nu(n). In this paper we develop an inverse Littlewood-Offord theory (somewhat in the spirit of Freiman's inverse theory in additive combinatori...
-
作者：Bridson, Martin R.; Howie, James; Miller, Charles F., III; Short, Hamish
摘要：If Gamma(1), ... , Gamma(n) are limit groups and S subset of Gamma(1) x ... x Gamma(n) is of type FPn (Q) then S contains a subgroup of finite index that is itself a direct product of at most n limit groups. This answers a question of Sela.
-
作者：De Lellis, Camillo; Szekelyhidi, Laszlo, Jr.
摘要：We propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in R-n with n >= 2. We give a reformulation of the Euler equations as a differential inclusion, and in this way we obtain transparent proofs of several celebrated results of V. Scheffer and A. Shnirelman concerning the non-uniqueness of weak solutions and the existence of energy-decreasing solutions. Our results are stronger because they work in any dimension and yiel...
-
作者：Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
摘要：We prove the B. and M. Shapiro conjecture that if the Wronskian of a set of polynomials has real roots only, then the complex span of this set of polynomials has a basis consisting of polynomials with real coefficients. This, in particular, implies the following result: If all ramification points of a parametrized rational curve phi : CP1 -> CPr lie on a circle in the Riemann sphere CP1, then phi maps this circle into a suitable real subspace RPr subset of CPr. The proof is based on the Bethe ...
-
作者：Frenkel, Edward; Gross, Benedict
摘要：In this paper we construct a connection del on the trivial G-bundle on P-1 for any simple complex algebraic group G, which is regular outside of the points 0 and infinity, has a regular singularity at the point 0, with principal unipotent monodromy, and has an irregular singularity at the point infinity, with slope 1/h, the reciprocal of the Coxeter number of G. The connection del, which admits the structure of an oper in the sense of Beilinson and Drinfeld, appears to be the characteristic 0 ...
-
作者：Hingston, Nancy
摘要：Let the torus T-2n be equipped with the standard symplectic structure and a periodic Hamiltonian H is an element of C-3(S-1 x T-2n, R). We look for periodic orbits of the Hamiltonian flow (u) over dot(t) = J del H(t, (t)). A subharmonic solution is a periodic orbit with minimal period an integral multiple in of the period of H, with in > 1. We prove that if the Hamiltonian flow has only finitely many orbits with the same period as H, then there are subharmonic solutions with arbitrarily high m...
