Lattice cohomology and rational cuspidal curves
نویسندگان
چکیده
منابع مشابه
Rational Cuspidal Curves
It is the product of my playing with beautiful geometric objects called rational cuspidal curves over the past two years. I would like to thank everyone who has contributed to this thesis. I owe so much to everyone who has ever taught me mathematics. Thank you for inspiring me and for providing me with the skills necessary to complete this thesis. To my friends and fellow students at Abel, than...
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Let A be an elliptic curve over Q of square free conductor N . Suppose A has a rational torsion point of prime order r such that r does not divide 6N . We prove that then r divides the order of the cuspidal subgroup C of J0(N). If A is optimal, then viewing A as an abelian subvariety of J0(N), our proof shows more precisely that r divides the order of A ∩ C. Also, under the hypotheses above, we...
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A cuspidal curve is a curve whose singularities are all cusps, i.e. unibranched singularities. The article describes computations which lead to the following conjecture: A rational cuspidal plane curve of degree greater or equal to six has at most three cusps. The curves with precisely three cusps occur in three series. Assuming the Flenner–Zaidenberg rigidity conjecture the above conjecture is...
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We compute the Euler characteristics of the moduli spaces of abelian vortices on curves with nodal and cuspidal singularities. This generalizes our previous work where only nodes were taken into account. The result we obtain is again consistent with the expected reconciliation between the vortex picture of D2-D0 branes and the proposal by Gopakumar and Vafa.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2016
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2016.v23.n2.a3