scholarly journals On the formal principle for curves on projective surfaces

Author(s):  
Jorge Vitório Pereira ◽  
Olivier Thom
2017 ◽  
Vol 28 (2) ◽  
pp. 270-284
Author(s):  
Olga Nikolic ◽  
Igor Cvejic

The aim of this paper is to show, contra the right-libertarian critique of social justice, that there are good reasons for defending policies of social justice within a free society. In the first part of the paper, we will present two influential right-libertarian critiques of social justice, found in Friedrich Hayek?s Law, Legislation and Liberty and Robert Nozick?s Anarchy, State and Utopia. Based on their approach, policies of social justice are seen as an unjustified infringement on freedoms of individual members of a society. In response to this critique, we will introduce the distincion between formal and factual freedom and argue that the formal principle of freedom defended by Hayek and Nozick does not suffice for the protection of factual freedom of members of a society, because it does not recognize (1) the moral obligation to help those who, without their fault, lack factual freedom to a significant degree, and (2) the legal obligation of the state to protect civic dignity of all members of a society. In the second part of the paper, we offer an interpretation of Kant?s argument on taxation, according to which civic dignity presupposes factual freedom, in order to argue that Kant?s justification of taxation offers good reasons for claiming that the state has the legal obligation to protect factual freedom via the policies of social justice.


Author(s):  
Nate Gillman ◽  
Xavier Gonzalez ◽  
Ken Ono ◽  
Larry Rolen ◽  
Matthew Schoenbauer

We celebrate the 100th anniversary of Srinivasa Ramanujan's election as a Fellow of the Royal Society, which was largely based on his work with G. H. Hardy on the asymptotic properties of the partition function. After recalling this revolutionary work, marking the birth of the ‘circle method’, we present a contemporary example of its legacy in topology. We deduce the equidistribution of Hodge numbers for Hilbert schemes of suitable smooth projective surfaces. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.


2017 ◽  
Vol 28 (14) ◽  
pp. 1750106
Author(s):  
Maciej Borodzik

We study rational cuspidal curves in projective surfaces. We specify two criteria obstructing possible configurations of singular points that may occur on such curves. One criterion generalizes the result of Fernandez de Bobadilla, Luengo, Melle–Hernandez and Némethi and is based on the Bézout theorem. The other one is a generalization of the result obtained by Livingston and the author and relies on Ozsváth–Szabó inequalities for [Formula: see text]-invariants in Heegaard Floer homology. We show by means of explicit calculations that the two approaches give very similar obstructions.


2003 ◽  
Vol 173 (1) ◽  
pp. 144-177 ◽  
Author(s):  
Daniel Chan ◽  
Rajesh S. Kulkarni

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