On linear series with negative Brill-Noether number

Brill-Noether theory studies the existence and deformations of curves in projective spaces; its basic object of study is $\mathcal{W}^r_{d,g}$, the moduli space of smooth genus $g$ curves with a choice of degree $d$ line bundle having at least $(r+1)$ independent global sections. The Brill-Noether theorem asserts that the map $\mathcal{W}^r_{d,g} \rightarrow \mathcal{M}_g$ is surjective with general fiber dimension given by the number $\rho = g - (r+1)(g-d+r)$, under the hypothesis that $0 \leq \rho \leq g$. One may naturally conjecture that for $\rho < 0$, this map is generically finite onto a subvariety of codimension $-\rho$ in $\mathcal{M}_g$. This conjecture fails in general, but seemingly only when $-\rho$ is large compared to $g$. This paper proves that this conjecture does hold for at least one irreducible component of $\mathcal{W}^r_{d,g}$, under the hypothesis that $0 < -\rho \leq \frac{r}{r+2} g - 3r+3$. We conjecture that this result should hold for all $0 < -\rho \leq g + C$ for some constant $C$, and we give a purely combinatorial conjecture that would imply this stronger result.Comment: 16 page

Book Review: \u3cem\u3eSacred Matters: Material Religion in South Asian Traditions\u3c/em\u3e

Book Review of Sacred Matters: Material Religion in South Asian Traditions. Edited by Tracy Pintchman and Corinne G. Dempsey. Albany: State University of New York Press, 2015, xi + 221 pp

Optimal agglomeration and regional policy

This paper studies the social desirability of agglomeration and the efficiency arguments for regional policy in a simple, analytically solvable ‘new economic geography’ model with two trade integrating regions. The location pattern emerging as market equilibrium is ?-shaped, featuring dispersion of firms both at high and low trade costs and stable equilibria with partial agglomeration of firms in addition to core periphery equilibria for intermediate levels of trade costs. Our central finding is that the market equilibrium is characterised by over-agglomeration for high trade costs and under-agglomeration for low trade costs. For an intermediate level of trade costs, the market equilibrium yields the socially optimal degree of agglomeration. An important implication of this result is that, on efficiency grounds, regional policy should foster the dispersion of firms for a range of high trade costs only, but agglomeration for a range of low trade costs. Hence, regional policies, such as those pursued by the European Union (which are aimed at fostering dispersion in general), is counterproductive when trade integration is deep enough JEL-Classification: F12, F15, F22, R12, R50 Keywords: economic geography, regional policy, optimal agglomeration, welfare

South Dakota Agricultural Land Market Trends 1991–2008

The 2008 SDSU Farm Real Estate Market Survey report contains information on current agricultural land values and cash rental rates by land use in different regions of South Dakota, with comparisons to values from earlier yearsland values, Acreage, Agricultural Land, Cropland, Farmland, Farms, Land Ownership