It was conjectured in [Nam73] that the Torelli map Mg → Ag associating to a curve its jacobian extends to a regular map from the DeligneMumford moduli space of stable curves Mg to the (normalization of the) Igusa blowup A cent g . A counterexample in genus g = 9 was found in [AB11]. Here, we prove that the extended map is regular for all g ≤ 8, thus completely solving the problem in every genus.

Let a be a non-invertible transformation of a finite set and let G be a group of permutations on that same set. Then 〈G, a 〉 \G is a subsemigroup, consisting of all non-invertible transformations, in the semigroup generated by G and a. Likewise, the conjugates ag = g−1ag of a by elements g ∈ G generate a semigroup denoted 〈ag | g ∈ G〉. We classify the finite permutation groups G on a finite set...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

Different external representations for learning and solving mathematical operations may affect learning and transfer. To explore the effects of learning representations, learners were each introduced to two new operations (b↑n and b↓n) via either formulas or graphical representations. Both groups became adept at solving regular (trained) problems. During transfer, no external formulas or graphs...

When incorporated in membranes, Ag0 nanoparticles are effective antifouling and antibacterial agents, arising from the presence of Ag+ ions either in solution or adsorbed onto nanoparticles. A vari...

(i) A subgroup of PFL(d, q) containing PSL(d, q), in its usual 2-transitive representation; (ii) A collineation group of AG(d, q), containing the group ASL(d, q) of collineations generated by elations, in its usual 2-transitive representation on AG(d, q); (iii) A 7 in its 2-transitive representation of degree 15; (iv) There is a regular normal subgroup, and if x~S then F x acts on S { x } as th...

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

We examined whether there are crosscultural differences in the magnitude of genetic and environmental contributions to risk of becoming a regular smoker and of persistence in smoking in men and women. Standard methods of epidemiologic and genetic analysis were applied to questionnaire data on history of cigarette use obtained from large samples of male and female like-sex twins from three diffe...

We show that the excluded minors for the class of matroids that are binary or ternary are U2,5, U3,5, U2,4⊕F7, U2,4⊕F ∗ 7 , U2,4⊕2F7, U2,4 ⊕2 F ∗ 7 , and the unique matroids obtained by relaxing a circuithyperplane in either AG(3, 2) or T12. The proof makes essential use of results obtained by Truemper on the structure of almost-regular matroids.