A wall-crossing formula for degrees of Real central projections
2014 ◽
Vol 25
(04)
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pp. 1450038
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Keyword(s):
The main result is a wall-crossing formula for central projections defined on submanifolds of a Real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the degree depends on the projection is a new phenomenon, specific to Real algebraic geometry. We illustrate this phenomenon in many interesting situations. The crucial assumption on the class of maps we consider is relative orientability, a condition which allows us to define a ℤ-valued degree map in a coherent way. We end the article with several examples, e.g. the pole placement map associated with a quotient, the Wronski map, and a new version of the Real subspace problem.
Keyword(s):
1973 ◽
Vol 23
(1)
◽
pp. 95-101
1974 ◽
Vol 26
(1)
◽
pp. 161-167
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1971 ◽
Vol 23
(6)
◽
pp. 1102-1115
◽
Keyword(s):
Keyword(s):
2018 ◽
Vol 2020
(17)
◽
pp. 5450-5475
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2001 ◽
Vol 353
(5)
◽
pp. 1959-1970
◽
1986 ◽
Vol 22
(1)
◽
pp. 81-95
◽
1999 ◽
Vol 42
(3)
◽
pp. 307-320
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Keyword(s):