For a smooth curve of genus g embedded by a line bundle of degree at least 2g + 3 we show that the ideal sheaf of the secant variety is 5-regular. This bound is sharp with respect to both the degree of the embedding and the bound on the regularity. Further, we show that the secant variety is projectively normal for the generic embedding of degree at least 2g + 3. AMS Subject Classification (200...

We solve the following problem: Let M be a 2g × 2g symplectic matrix of prime order with integer entries. Find a unique normal form for M , that is, a symplectic matrix whose entries are determined by its conjugacy invariants. This is equivalent to finding a unique normal form for the matrix representation of the conjugacy class of a prime order element of the mapping class group.

CONTEXT Reliable thyroglobulin (Tg) autoantibody (TgAb) detection before Tg testing for differentiated thyroid cancer (DTC) is critical when TgAb status (positive/negative) is used to authenticate sensitive second-generation immunometric assay ((2G)IMA) measurements as free from TgAb interference and when reflexing "TgAb-positive" sera to TgAb-resistant, but less sensitive, Tg methodologies (ra...

We apply topological methods to study eigenvalues of the Laplacian on closed hyperbolic surfaces. For any closed hyperbolic surface S of genus g , we get a geometric lower bound on 2g 2.S/ W 2g 2.S/ > 1=4C 0.S/ > 0; where 0.S/ is an explicit constant which depends only on the systole of S . Mathematics Subject Classification (2010). Primary 30F; Secondary 35P05, 35P15.

We investigate closed subgroups $$G \subseteq \mathrm {Sp}_{2g}(\mathbb {Z}_2)$$ whose modulo-2 images coincide with the image $$\mathfrak {S}_{2g + 1} {F}_2)$$ of $$S_{2g 1}$$ or 2} 2}$$ under standard representation. show that when $$g \ge 2$$ , only subgroup surjecting onto is its full inverse in $$\mathrm while all are open and contain level-8 principal congruence . As an immediate applicat...

Let $$\mathscr {C}$$ be a hyperelliptic curve of genus $$g>1$$ over an algebraically closed field K characteristic zero and {O}$$ one the $$(2g{+}2)$$ Weierstrass points in {C}(K)$$ . J Jacobian , which is g-dimensional abelian variety K. us consider canonical embedding into that sends to group law on J. This allows identify with certain subset commutative J(K). A special case famous theorem Ra...

Many people who have tried to configure their IEEE 802.11 enabled mobile phones to connect to a public wireless hotspot know one of the major differences between IEEE 802.11 networks and 2G: the missing standardized login process. While the 2G standard covers all aspects of the communication process, first IEEE 802.11 standards only targeted the data transmission. Due to this lack of standards ...

Laser ablation–inductively coupled plasma – mass spectrometry (LA–ICP–MS) is a powerful tool for determining the elemental and isotopic compositions of various samples. The disadvantage LA–ICP–MS that it consumes more sample material than other types in situ analytical methods. To extend application this method to trace element analysis, we conducted single-pulse analysis Reference Materials Na...